Semi-rigid Connections Handbook - Wai-Fah Chen

semi-rigid connections handbook Edited by

Wai-Fah Chen Norimitsu Kishi Masato Komuro

Copyright © 2011 by J. Ross Publishing, Inc. ISBN: 978-1-932159-99-8 Printed and bound in the U.S.A. Printed on acid-free paper 10 9 8 7 6 5 4 3 2 1

Library of Congress Cataloging-in-Publication Data Semi-rigid connections handbook / edited by Wai-Fah Chen, Norimitsu Kishi, and Masato Komuro. p. cm. — (J. Ross Publishing civil & environmental engineering series) Includes bibliographical references and index. ISBN 978-1-932159-99-8 (hardcover : alk. paper) 1. Columns, Iron and steel--Specifications. 2. Steel framing (Building) 3. Deformations (Mechanics) 4. Structural dynamics. I. Chen, Wai-Fah, 1936- II. Kishi, Norimitsu, 1949- III. Komuro, Masato, 1969 TA492.C7S46 2010 624.1’772--dc22 2010035278 This publication contains information obtained from authentic and highly regarded sources. Reprinted material is used with permission, and sources are indicated. Reasonable effort has been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use. All rights reserved. Neither this publication nor any part thereof may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the publisher. The copyright owner’s consent does not extend to copying for general distribution for promotion, for creating new works, or for resale. Specific permission must be obtained from J. Ross Publishing for such purposes. Direct all inquiries to J. Ross Publishing, Inc., 5765 N. Andrews Way, Fort Lauderdale, FL 33309. Phone: (954) 727-9333 Fax: (561) 892-0700 Web: www.jrosspub.com

CIVIL AND ENVIRONMENTAL ENGINEERING SERIES Wai-Fah Chen, Editor-in-Chief

Semi-rigid Connections Handbook by Wai-Fah Chen, Norimitsu Kishi, and Masato Komuro Elastic Beam Calculations Handbook by Jih-Jiang Chyu Deepwater Foundations and Pipeline Geomechanics by William O. McCarron Sulfur Concrete for the Construction Industry: A Sustainable Development Approach by Abdel-Mohsen Onsy Mohamed and Maisa El Gamal

Contents

Preface.......................................................................................................................................vii About the Editors.......................................................................................................................ix

Section I. Specifications and Classifications

1 Classification and AISC Specification...................................................................................1 1.1 Classification of Connections......................................................................................................1 1.2 AISC Specification.......................................................................................................................22 References.....................................................................................................................................26

Section II. Effects of Semi-rigid Connections on Structural Members and Frames

2 Effects of Semi-rigid Connections on Structural Members and Frames............................27 2.1 Introduction.................................................................................................................................27 2.2 Effects of Semi-rigid Connections on Columns......................................................................32 2.3 Effects of Semi-rigid Connections on Beams..........................................................................40 2.4 Effects of Semi-rigid Connections on Frames.........................................................................45 2.5 Summary and Conclusions........................................................................................................67 References.....................................................................................................................................68

Section III. Steel Connection Database and Modeling

3 Types of PR Connections.....................................................................................................71 3.1 Single Web-angle Connections/Single Plate Connections.....................................................71 3.2 Double Web-angle Connections................................................................................................71 3.3 Top- and Seat-angle Connections with Double Web-angle...................................................73 3.4 Top- and Seat-angle Connections.............................................................................................73 3.5 Extended End-plate Connections/Flush End-plate Connections.........................................75 3.6 Header Plate Connections..........................................................................................................75 References.....................................................................................................................................77 4 Modeling of Connections.....................................................................................................79 4.1 General Remarks.........................................................................................................................79 4.2 Behavior Under Monotonic Loading........................................................................................80 4.3 Behavior Under Cyclic Loading.................................................................................................89 References.....................................................................................................................................92 5 Steel Connection Database...................................................................................................95 5.1 General Remarks.........................................................................................................................95 5.2 Parameter Definition for Connection Type...........................................................................100 5.3 Steel Connection Databank Program.....................................................................................129 v

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Semi-rigid Connections Handbook

5.4 Web site of Connections...........................................................................................................132 References...................................................................................................................................140

Section IV. Steel-concrete Composite Connections

6 Advanced Analysis of Steel and Composite Semi-rigid Frames........................................143 6.1 Structural Frames......................................................................................................................143 6.2 Advanced Analysis of Steel Frames.........................................................................................154 6.3 Advanced Analysis of Composite Frames..............................................................................211 Appendix 1 Elastic Stiffness Matrix, ke.........................................................................................252 Appendix 2 Geometric Stiffness Matrix, kg..................................................................................253 Appendix 3 Bowing Matrix, kb. .....................................................................................................254

Section V. Case Study

7 Case Studies for Second-order (Direct) Analysis of Semi-rigid Frames in Hong Kong......................................................................................................................255 7.1 Introduction...............................................................................................................................255 7.2 Second-order Integrated Design and Analysis......................................................................256 7.3 Modeling of Semi-rigid Jointed Members..............................................................................257 7.4 Examples.....................................................................................................................................259 7.5 Conclusions................................................................................................................................268 References...................................................................................................................................268 Appendix Experimental Data of SCDB A-1 Single Web Angle/Single Plate Connections..................................................................... A1-1 A-2 Double Web-Angle Connections........................................................................................ A2-1 A-3 Top- and Seat-angle with Double Web-angle Connections............................................. A3-1 A-4 Top- and Seat-angle Connections....................................................................................... A4-1 A-5 Extended End-plate Connections....................................................................................... A5-1 A-6 Flush End-plate Connections.............................................................................................. A6-1 A-7 Header End-plate Connections........................................................................................... A7-1 Index.........................................................................................................................................I-1

Preface

The steel framework is one of the most commonly used structural systems in modern construction. The analysis of such structural systems is governed by the assumptions adopted in the modeling of their structural elements, especially those concerning the behavior of beam-to-column connections. Conventional analysis and design of this framework are performed using the assumption of a fully rigid or ideally pinned connection. The assumption of a fully rigid connection implies that no relative rotation of the connection occurs and the end moment of the beam is completely transferred to the column. On the other hand, the pinned connection implies that no restraint for rotation of the connection exists and the connection moment is always zero. The popularity of these idealized models results from the fact that they are simple to use and easy to implement in the analysis and design of steel frameworks. However, as evident from experimental observations, all beam-to-column connections used in current practice possess some stiffness and fall between the two extreme cases of fully rigid and ideally pinned. In general, the connection that welds the beam directly to the flange of the column is considered fully rigid. However, the connection that fastens the beam to the column with some top and bottom angles and a web plate or with all angles, using either bolts or rivets, (with some angles and/or a plate, bolts or rivets,) displays a nonlinear behavior and lies somewhere between the fully rigid and perfectly pinned conditions, commonly called semi-rigid connections. The nonlinear semi-rigid connection behaviors can be seen clearly in many experimental results. On the other hand, single and double web-angles and header plate connections generally have much less connection stiffness and may be treated as pinned connections. The end-plate connection has connection stiffness close to that of a rigid condition, while the top- and seat-angle connection lies somewhere in between these two extremes and is usually treated as a semi-rigid connection. The recent development of the limit-state approach to design has focused particular attention on the limits of resistance and serviceability. To this end, we need accurate information regarding the behavior of structures throughout the entire range of loading up to ultimate load considering the characteristics of connection stiffness. Research on the topic of steel frames with semi-rigid connections (Partially Restrained (PR) construction or PR connection) has been conducted over the past 20 years. Despite significant research and development efforts, usage of PR principles has nevertheless been slow in coming to the profession caused in part by the lack of easy access to reliable test data on these connections and also due to the lack of software for practical implementation. With the publication of the 2005 AISC specifications as well as Eurocode 3, practical implementation of the use of PR connections in structural systems is now a real possibility. This handbook presents a simple and comprehensive introduction that will help design practitioners implement these new developments into engineering practice. Beginning with a discussion of the new specifications and classifications of these connections, we go on to show (on the basis of the collected connections database) practical mathematical models for computer implementation and provide case studies on these frames including composite construction. With the help of the user-friendly list of collected data in tabular vii

viii


form with illustrative figures, information on semi-rigid connections is now available in a single publication and may ultimately result in its widespread usage among practitioners. The scope of the book is indicated by the table of contents with the following features: • Introduces the 2005 AISC specifications with a cross reference to the counterpart of the new Eurocode 3 on semi-rigid construction • Includes more than 700 semi-rigid connection test data in tabular form with figures • Provides connection models for analysis and design with case studies • Includes the recent development of steel-concrete composite connections with case studies We are grateful to the following contributors for their advice, help, and original work at various stages during the preparation of the book: S. L. Chan, Y. Goto, J. Y. R. Liew, and E. Lui. W. F. Chen N. Kishi M. Komuro

About the Editors

Dr. Wai-Fah Chen is a well-respected leader in the field of plasticity, structural stability, and structural steel design over the past half century. Having headed the engineering school and department at the University of Hawaii and Purdue University, Chen is a widely cited author for his contributions in the fields of mechanics, materials, and computing. He is the author or coauthor of 20 engineering books and the recipient of several national engineering awards, including the 1990 Shortridge Hardesty Award from the American Society of Civil Engineers and the 2003 Lifetime Achievement Award from the American Institute of Steel Construction. He is a member of the U.S. National Academy of Engineering and an honorary member of the American Society of Civil Engineers. Dr. Norimitsu Kishi received his Ph.D. in civil engineering from Hokkaido University-Japan in 1977. From March 1985 to March 1986, he was an overseas researcher at Purdue University under Professor W. F. Chen. He is currently professor and director of the Structural Mechanics Laboratory in the Department of Civil Engineering and Architecture at the Muroran Institute of Technology-Japan. Dr. Masato Komuro graduated with a degree in civil engineering in 1992 from the Muroran Institute of Technology-Japan, where he also obtained his Ph.D. in structural engineering in 2001. From May 2007 to April 2008, he was a visiting researcher in the Department of Civil & Environmental Engineering at the University of Hawaii-Manoa. He is currently assistant professor in the Department of Civil Engineering and Architecture at the Muroran Institute of Technology.

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Contributors S. L. Chan Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Hong Chen Offshore Technology Development Pte Ltd, Keppel Offshore & Marine, Singapore Yoshiaki Goto Dr. Eng. Professor, Department of Civil Engineering, Nagoya Institute of Technology, Japan Dennis Lam Department of Civil Engineering, University of Leeds, U.K. J. Y. Richard Liew Department of Civil Engineering, National University of Singapore, Singapore Y. P. Liu Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong Eric M. Lui Meredith Professor, Department of Civil and Environmental Engineering, Syracuse University, NY Zhiling Zhang Graduate Student, Department of Civil and Environmental Engineering, Syracuse University, NY

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At J. Ross Publishing we are committed to providing today’s professional with practical, hands-on tools that enhance the learning experience and give readers an opportunity to apply what they have learned. That is why we offer free ancillary materials available for download on this book and all participating Web Added Value™ publications. These online resources may include interactive versions of material that appears in the book or supplemental templates, worksheets, models, plans, case studies, proposals, spreadsheets, and assessment tools, among other things. Whenever you see the WAV™ symbol in any of our publications, it means bonus materials accompany the book and are available from the Web Added Value™ Download Resource Center at www.jrosspub. com. Downloads for Semi-rigid Connections Handbook consist of updated connection data, the Steel Connection Data Bank (SCDB) program, references, and a link to the semi-rigid website at the Muroran Institute of Technology, Japan.

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1

Classification and AISC Specification

Yoshiaki Goto Dr. Eng. Professor, Department of Civil Engineering, Nagoya Institute of Technology, Japan

1.1 Classification of Connections...................................................................................................1 General • Eurocode 3 Classification System (CEN 2005) • AISC Classification System (AISC 2005) • Bjorhovde et al. Classification System • Nethercot et al. Classification System • Goto et al. Classification System • Comparison of Existing Classification Systems 1.2 AISC Specification.................................................................................................................. 22 Introduction • Connection Classification • Structural Analysis and Design for Frames with PR Connections References......................................................................................................................................... 26

1.1 Classification of Connections 1.1.1 General

A beam-to-column connection is generally subject to axial force, shear force, and bending moment for its in-plane behavior. However, the deformation of the connection caused by axial and shear forces are usually small when compared to the deformation caused by bending moment. Consequently, for practical purposes, only the effect of moment on the rotational deformation of connections shown in Figure 1.1 needs to be considered. The in-plane behavior of connections can be represented by the moment-rotation (M–θr ) curves illustrated in Figure 1.2. All types of actual beam-to-column connections possess some rotational stiffness that falls between the two extreme cases of fully rigid and ideally pinned. Thus, the modeling of connections as semi-rigid is more realistic. However, in engineering practice, some connections can be considered pinned if their stiffness is so small that the connections are incapable of transmitting any significant moment, thus permitting almost free rotation. Similarly, some connections can be considered rigid if their rigidity is so large that no significant slope discontinuity exists between the adjoining members. The assumption of ideally pinned or rigid connections considerably simplifies the design and analysis procedures of framed structures. For that reason, it is beneficial and practical to estimate whether the connec-

1

2


θr

Column Beam

M

FIGURE 1.1 Rotational deformation of a connection.

tions can be assumed rigid, semi-rigid, or pinned. The classification of connections should be made based on the behavior of the frames at serviceability and ultimate-limit states. Primary index properties that govern the moment-rotation characteristics of connections are stiffness, strength, and rotational capacity. These properties are important factors that are used for the classification. However, the requirement for strength and rotational capacity of connections is not always necessary. This is because the strength and rotational capacity of connections are determined during the design procedure, such that they exceed the calculated moment and rotation demand at the ultimate-limit state of frames. The classification systems of connections have been presented by Bjorhovde et al. (1990), Goto et al. (1998), Nethercot et al. (1998), Eurocode 3 (CEN, 2005), and ANSI/AISC360-06 (AISC, 2005). The following explains and discusses these existing classification systems.

1.1.2 Eurocode 3 Classification System (CEN 2005)

Eurocode 3 (2005) models connections as simple, semicontinuous, and continuous in structural analysis. In the simple connection model, a connection is assumed not to transmit bending moment and may be modeled as ideally pinned. In the semicontinuous connection model, the behavior of a connection has to be taken into account and modeling of the so-called semi-rigid


3

θr

Moment, M

Column

T-stub

M

Beam

End Plate

Top and Seat Angle

Header Plate

Double Web Angle Single Web Angle Rotation, θr FIGURE 1.2 Moment-rotation curves of semi-rigid connections.

connection is necessary in the structural analysis. In the continuous connection model, the behavior of a connection is assumed to have no effect on the analysis and may be modeled as so-called rigid. The above three types of connection models are classified based on the two independent criteria expressed in terms of rotational stiffness and strength, respectively. The scheme of modeling of connections is shown in Table 1.1, specifically for the case of nonlinear elastic-plastic structural analysis. This is because the types of connection models used in this analysis are determined based on both stiffness and strength of a connection in contrast to

4


TABLE 1.1 Types of EC3 connection models used in elastic-plastic structural analysis Type of connection model

Classification by stiffness1

Classification by strength2

Continuous

Rigid

Full strength

Semi-continuous

Rigid

Partial strength

Semi-rigid

Full strength Partial strength

Simple

Nominally pinned

Nominally pinned

Remarks: 1) See Table 1.2; 2) See Table 1.3

those used in elastic analysis or rigid-plastic analysis where either stiffness or strength is considered in the determination of connection modeling. As shown in Table 1.2, connections are classified as rigid, semi-rigid, or nominally pinned based on the initial rotational stiffness Rki of connections. The boundary between rigid and semirigid connections is determined, such that the load-carrying capacity of a semi-rigid portal frame is higher than 95 percent of the strength of the corresponding rigid frame. A frame model used to calculate the load-carrying capacity is a pin-based portal frame shown in Figure 1.3. The load carrying capacity is estimated by the Marchant-Rankin formula (Horne and Merchant, 1965). Since the effect of connection stiffness on the frame strength is dependent on whether the frame is braced or unbraced, the boundaries for the classification of connections are differently specified for these two types of frames. These boundaries are expressed in terms of a nondimensional initial connection stiffness parameter kb defined as kb = Rki /(EIb/Lb). Similar to the classification based on the rotational stiffness, connections are classified as full strength, partial strength or nominally pinned, depending on the ratio between the design mo-

TABLE 1.2 EC3 classification of connections by stiffness Connections Rigid Semi-rigid

kb = Rki /(EIb/Lb) Braced frames

8 < kb

Unbraced frames

25 < kb

Braced frames

0.5 ≤ kb ≤ 8

Unbraced frames Nominally pinned

25 < kb

Other requirement Kb/Kc ≥ 0.1 Kb/Kc < 0.1

0.5 ≤ kb ≤ 25 kb < 0.5

Remarks: Braced frames = those where the bracing system reduces the horizontal displacement by at least 80% Rki = initial rotational stiffness of connections Kb = the mean value of Ib /Lb for all the beams at the top of that story Kc = the mean value of Ic /Lc for all the columns in that story Ib = the second moment of inertia of a beam Ic = the second moment of inertia of a column Lb = the span of a beam Lc= the story height of a column


5

Fc

Fc

EIb Rk

EIc

EIc

Lc

Lb FIGURE 1.3 Pin-based portal frame.

ment resistance of connections Mj,Rd and the design plastic moment resistance of the connected members such as beams Mb,pl,Rd and columns Mc,pl,Rd. The boundaries for this classification are different according to whether the connections are located at the top of columns or within the height of columns (Figure 1.4). The classification based on the connection strength is summarized in Table 1.3. Although the required rotational capacity of connections is not specified in EC3 classification, being different from the classifications by Bjorhovde et al. (1990), Goto et al. (1998) and Nethercot et al. (1998), the connections must be designed such that the deformation of connections imposed by the internal forces and moment is within the deformation capacity of the connections. An almost similar scheme is adopted by the AISC specification (AISC, 2005). EC3 considers the behavior of frames at the ultimate-limit state in the classification of connections. However, it does not explicitly take into account the behavior at the serviceability limit state. Furthermore, in the evaluation of the load-carrying capacity of frames, EC3 adopts an approximate formula (i.e., the Merchant-Rankine formula). In addition, a single-story portal frame model used in this evaluation may be too simple to reflect the effect of layout and member details of frames in practice.

a

Mj,Rd

b

Mj,Rd

FIGURE 1.4 Full-strength of connections: (a) top of column; (b) within column height.

6


TABLE 1.3 EC3 classification of connections by strength Connection Fullstrength

Partialstrength

Nominally pinned

Mj,Rd

Top of column

 M j ,Rd M j ,Rd  1.0 ≤  or  M c ,pl ,Rd   M b ,pl ,Rd

Within column height

 M j ,Rd M j ,Rd  1.0 ≤  or  2M c ,pl ,Rd   M b ,pl ,Rd

Top of column

 M j ,Rd M j ,Rd  0.25 <  and  < 1.0 M M  b ,pl ,Rd c ,pl ,Rd 


 M j ,Rd M j ,Rd  0.25 <  and  < 1.0 2M c ,pl ,Rd   M b ,pl ,Rd

Top of column

 M j , Rd M j ,Rd  or   ≤ 0.25 M M  b ,pl ,Rd c ,pl ,Rd 


 M j , Rd M j ,Rd  or   ≤ 0.25 2M c ,pl ,Rd   M b ,pl ,Rd

Other requirements

1. Capable of transmitting internal forces without developing significant moment that might adversely affect the members or the structure as a whole 2. Capable of accepting the resulting rotation under the design load

Remarks: Mj,Rd = the design moment resistance of a connection Mb,pl,Rd = the design plastic moment resistance of the connected beam Mc,pl,Rd = the design plastic moment resistance of the connected column

A precise elastic-plastic finite-displacement analysis showed that the EC3 boundary between rigid and semi-rigid connections is on the whole restrictive in terms of the ultimate strength of frames (Goto and Miyashita, 1995).

1.1.3 AISC Classification System (AISC 2005)

AISC specification classifies connections as fully restrained (FR), partially restrained (PR), and simple connections, based on the secant stiffness Rks at service load and the strength Mn, respectively, of a connection, as summarized in Table 1.4. This classification is applied to both sway and nonsway frames. Simple and FR connections may be idealized as pinned and rigid, respectively, for the purpose of structural analysis. For structures with PR connections, the connection flexibility must be estimated and included in the structural analysis by the semi-rigid connection model. The boundary between the fully restrained and partially restrained connections expressed in terms of the secant connection stiffness parameter RksLb/EIb at the service load is determined such that the ratio of the connection moment obtained from semi-rigid analysis to that obtained from rigid analysis is 90 percent. Lb and EIb are the length and bending rigidity of the connected beam. The connection moment to determine the classification boundary is calculated by using a simple beam with semi-rigid connections at both ends, as shown in Figure 1.5 (Leon, 1994).


7

TABLE 1.4 AISC classification of connections Connections

Stiffness

Strength

Ductility

RksLb /EIb ≤ 2

• Satisfy shear force demand at strength-limit state

• Satisfies rotation demand at the strengthlimit state or

• M ≤ 0.02 Mpb at 0.02 radians

• vu = 0.03 radians

• Satisfy combined shear force and moment demand at strength-limit state


• Satisfy combined shear force and moment demand at strength-limit state


Simple

2 < RksLb /EIb < 20 PR

FR

With partialstrength of connected beam

20 ≤ RksLb /EIb

• vu = 0.03 radians

• vu = 0.03 radians • No requirement

With fullstrength of connected beam

Remarks: Rks = secant stiffness of connections at service load Ib = second moment of inertia of beam Lb = span of beam E = Young’s modulus Mpb = plastic moment of beam vu = rotational capacity

As for the flexural strength Mn of connection, an explicit condition in the classification is imposed on the simple connections with no flexural strength. A connection with its moment of M ≤ 0.2Mpb (Mpb = fully plastic moment of the connected beam) at the rotation of 0.02 radians is considered to have no flexural strength for design analysis. The strengths of FR and PR connections must be adequate to resist the connection moment demand imposed by the design load. Therefore, it is possible in the AISC specification for an FR connection to have strength less than that of a connected beam. In this case, the semi-rigid action of the connection will appear if the plastification occurs in the connection. This implies that the rigid connection model is only

w Rk

Rk Lb

FIGURE 1.5 Simple beam with semi-rigid connections at both ends.

8


applicable before the plastication of the connection. It is also possible for a PR connection to have strength greater than that of the beam. Considering the above, the strength requirement for FR connections in the AISC is not as strict as that for rigid connections in EC3 where rigid connections must always have strength greater than the full strength of the connected beams or columns. The rotation capacity θu of connections is determined such that the rotation of connections at the strength-limit state of frames will not exceed θu. If the strength of a connection is substantially higher than that of the connected beam, the ductility of the structural system is controlled by the connected beam. However, if a connection has marginally higher or partial strength of the connected beam, the connection may experience some deformation before the structural system reaches its strength-limit state. In the above case, the ductility demand for FR, PR, and simple connections is calculated by a structural analysis in which the behavior of the connections is considered. This implies that the ductility required of the connection will depend on the particular application. In the absence of accurate analysis, the rotation capacity of 0.03 radians is considered adequate. The rotation capacity of connections defined by the AISC is explained in 1.2.2.4.

1.1.4 Bjorhovde et al. Classification System

A classification system proposed by Bjorhovde et al. (1990), as shown in Figure 1.6, is expressed in terms of nondimensional parameters of M/Mpb and θr/{Mpb(5d)/EIb}, where d and EIb are the depth and bending rigidity of the connected beam, respectively, and Mpb is the fully plastic moment capacity of the beam. As a reference beam length, 5d is assumed. Therefore, the initial stiffness of a connection is expressed in the form EIb/(ᾱd) where ᾱd is the equivalent length of the beam that gives the beam the same stiffness as the connection. If it is assumed that Lb is equal to 5d, the Bjorhovde’s classification parameter ᾱ is related to the EC3 (CEN, 2005) connection stiffness parameter kb as kb = 5/ᾱ. Based on the stiffness and strength of connections, connections are classified as rigid, semirigid, and flexible. Flexible connections may be modeled as ideally pinned in structural analysis. In addition, minimum rotational capacity inversely proportional to M/Mpb is specified for the respective connections. The Bjorhovde’s classification system is intended for the case where prior knowledge concerning the member and structural details is unavailable. M / Mpb

M=

EIb 2d

θr M=

1.0

EIb

10d

θr

Rigid 0.7

Ductility requirement

Semi-rigid 0.2 0

Flexible

θr 1.2

2.7

Mpb (5d) EIb

FIGURE 1.6 Classification (Bjorhovde et al., 1990).


9

However, this classification system is considerably approximate in nature, because it does not consider the overall behavior of frames. In fact, a precise elastic-plastic geometrically nonlinear analysis showed that the behavior of rigid frames in some cases is not assured by the Bjorhovde’s condition of rigid connections where the moment capacity of connections is higher than the 70 percent of the fully plastic moment of the connected beam (Goto and Miyashita, 1995).

1.1.5 Nethercot et al. Classification System

In this classification system, a classification of connections is made based on their stiffness, strength, and rotational capacity. The categories used in the classification are fully-connected, partially-connected, pin-connected and non-structural connections. These categories are specified both for serviceability and for ultimate-limit states as illustrated in Figures 1.7 and 1.8, respectively. In the classification, parameter α defined as α = 8(EIc/Lc)/(EIb/Lb) is considered for classification. Nethercot’s classification of connections considers the stiffness of a column and a beam that a connection is connecting. In the category of fully-connected connections, the behavior of connections is assumed not to affect the behavior of framed structures and may be modeled as so-called rigid. In the category of partially-connected connections, the behavior of connections has to be taken into account and modeling of the so-called semi-rigid connection is necessary in structural analysis. Pin-connected connections are not assumed to transmit bending moment and may be modeled as ideally pinned. The non-structural connections are those that do not satisfy the requirement for strength and rotational capacity. The non-structural connections are not regarded as a structural element. In the classification at the ultimate-limit state, as shown in Figure 1.8, the stiffness boundary between the fully-connected connection and partially-connected connection is determined such that the ratio of the connection moment obtained from semi-rigid analysis to that obtained from rigid analysis is 95 percent. In addition, the fully-connected connections and partially-connected connections with the stiffness kb = Rki/(EIb/Lb) greater than 1/(0.53 − 1/α) are required to have a moment capacity at least equal to the connected beam moment capacity. In this case, a required M / Mpb

fully-connected zone

1.0 2/3

0.25 0

partially-connected zone non-structual zone pin-connected zone 1/6-1/α

1/3

(7α−2)/(8α)

(20+12α+α2)/(70α2−20α) FIGURE 1.7 Classification at serviceability limit state (Nethercot et al., 1998).

θr Mpb Lb EIb

10


M / Mpb

fully-connected zone

1.0

partially-connected zone

non-structual zone 0.25 0

pin-connected zone 0.53−1/α

0.75/α+0.37

0.9

(2+α)/(38α)

θr Mpb Lb EIb

FIGURE 1.8 Classification at ultimate-limit state (Nethercot et al., 1998).

rotational capacity is not specified for connections, considering that the rotation will be mainly concentrated at the beam end. The stiffness boundary between partially-connected and pin-connected connections at the ultimate-limit state is calculated under the condition that the partially-connected connection moment is 25 percent of rigid connection moment. To obtain the connection moment, a single span subframe under uniformly distributed beam load as illustrated in Figure 1.9 is used. This subframe model may be interpreted as a subassemblage of nonsway frames. Since partially-connected connections and pin-connected connections generally undergo some amount of rotation, the minimum required rotational capacity, which is inversely proportional to M/Mpb is specified for the connections with the initial stiffness kb = Rki/(EIb/Lb) less than 1/(0.53 − 1/α). In the classification at the serviceability limit state shown in Figure 1.7, the stiffness boundary between the fully-connected and partially-connected connections is determined as kb = (70α2 − 20α)/ (20 + 12α + α2) such that the ratio of the beam displacement obtained from rigid frame analysis to that obtained from semi-rigid frame analysis is 90 percent. In addition, the fully-connected connections and partially-connected connections with the stiffness kb = Rki/(EIb/Lb) greater than (2/3)/ (1/6 − 1/α) are required to have a moment capacity that exceeds at least 2/3 of the connected-beam moment capacity. The stiffness boundary between partially-connected and pin-connected connections is calculated as kb = 2α/(7α − 2) under the condition that the beam deflection ratio between partially-connected connections and pin-connected connections is 90 percent. This boundary is applied to the range where θrEIb/(MpbLb) ≥ (7α − 2)/(2α). In the range θrEIb/(MpbLb) ≤ (7α − 2)/(2α), the strength boundary between partially-connected and pin-connected connections is given at the location of 25 percent of the connected beam moment capacity. Similar to the classification at the ultimate-limit state, the minimum rotational capacity inversely proportional to M/Mpb is specified for the partially-connected and pin-connected connections with the initial stiffness kb = Rki/(EIb/Lb) less than 2/{3(1/6 − 1/α)}. Although the rotational capacity and strength of connections are specified for both serviceability and ultimate-limit states in the Nethercot et al. classification system, the required rotational capacity and strength at the ultimate-limit state normally dominates. So, there is little reason to


11

EIc

EIc

Lc

EIb EIc

Rk

EIc

Lc

Lb FIGURE 1.9 Single-span subframe under uniformly distributed beam load.

specify these values in the classification at the serviceability limit states. Furthermore, it will be cumbersome to use different connection models in the frame analysis for design, depending on whether the limit state of concern is the ultimate or serviceability limit state.

1.1.6 Goto et al. Classification System

Goto et al. (1998) proposed a more detailed and precise classification system between rigid and semi-rigid connections considering the overall behavior of frames not only at the ultimate-limit state but also at the serviceability limit state. Herein, corrections are made to the mistakes in the original paper (Goto et al., 1998). In addition, a modification is made to improve the original classification scheme. To take into account the behavior of frames in the classification of connections, several subassemblages are used. These subassemblages approximately represent the behavior of the respective parts of the multistory multibay frames shown in Figure 1.10. The subassemblages are chosen by considering the deformation patterns of the respective parts of the sway and nonsway frames illustrated in Figure 1.11. The subassemblages so chosen are summarized in Figure 1.12 together with loading patterns. In this figure, the notations As ~ Fs and An ~ Fn are used to express the respective subassemblages that represent the parts of the frames in Figure 1.11.

12


Lb

Lc

Lc

Lc

Ic

Ic

Ic

Lb

Ib

Ic

Ib

Lb

Ib

Ic

Ib

Ic

Ic Ib

Ic

Ib

Ic

Column Lc: length Ic: second moment of inertia

Ib

Ic Beam

Lb: length Ib: second moment of inertia

Ib

Ic

Ib

Ic

(Pinned base)

: Connection

Lc

Ic

(Fixed base)

FIGURE 1.10 Multistory and multibay frame. Cs

As

Ds

Bs Es

Fs

(Pinned base)

Bs

Ds

(Fixed base)

a

An

Cn

Bn

Dn

En

Bn

Dn

Fn

(Pinned base)

(Fixed base)

b FIGURE 1.11 Deformation pattern of multistory, multibay frames: (a) sway; (b) nonsway.

(

)

(

)

V

V

P

Dn, Fn

column2

δs

beam2

}= loads at serviceability limit state

δs

beam1

column1

P = load at ultimate limit state

V H

Cn

column1

As, An Bs, Bn Cs, Cn Ds, Dn Es, En Fs, Fn Lc/2 Lc/2 Lc/2 Lc/2 Lc/2 Lc/2 Lc Lc/2 Lc Lc/2 --Lb/2 Lb/2 Lb/2 Lb/2 Lb/2 Lb/2 Lb/2 Lb/2 Lb/2 ----

Bn, En

δs

beam2

V

δs

Ds, Fs

column2

beam1

beam2

V

FIGURE 1.12 Subassemblages.

Note : As ~ Fs , An ~ Fn denote the subassemblages of multistory multibay frames shown in Fig. 1.11.

column1 column2 beam1 beam2

column2

beam1

H

P )

An

δs

beam1

V

(

column1

)

column1

Cs

δs

H

)

beam1

V

(

P

Bs, Es

column1

beam1

beam2

column1

(

P

As

column2

δs

H )

column1

δs

H

beam1

P

(

H

beam1

)

column1

)

P

(

P

(

P

Classification and AISC Specification 13

14


It is assumed that the initial connection stiffness affects the behavior of frames at the serviceability limit state and the boundary value of the initial stiffness between rigid and semi-rigid connections is derived based on the elastic displacement δs. This elastic displacement for sway subassemblages is calculated under horizontal force H, while elastic displacement for nonsway subassemblages are calculated under vertical force V. At the serviceability limit state, the effect of vertical compressive force P on the displacement δs is small; therefore, the elastic displacement is calculated by the small displacement theory, ignoring the effect of P. The criterion used to classify the connections as rigid is determined based on the tolerance Δ defined by (Equation 1.1): Δ = (δs − δr)/δr

(1.1)

where δs is a displacement of a subassemblage with semi-rigid connections and δr is a displacement of the corresponding rigid subassemblage. The boundary of the initial stiffness Rkib between rigid and semi-rigid connections so determined in terms of nondimentionalized initial stiffness parameter k bb = Rkib /(EIb/Lb) are summarized in Table 1.5, classified according to the respective types of subassemblages. In this table, to compare with EC3 boundary between rigid and semi-rigid connections, numerical results are also shown for Δ = 0.05 where G = (EIb/Lb)/(EIc/Lc) = 1.4 is assumed similar to the EC3 classification. In Table 1.5, the mistakes in the original paper (Goto et al., 1998) are corrected. To consider the connection behavior at the ultimate-limit state, the nonlinear moment-rotation relations are assumed to be expressed by the three-parameter model (Kishi et al.,1993) shown in Equation 1.2: m = muθ (1 + θ n )1/ n

(1.2)

TABLE 1.5 Goto et al. (1998) classification for initial stiffness of connections

k bb = Rkib / (EIb / Lb )

k bb = R bki / (EIb / Lb ) G = (EIb / Lb ) / (EIc / Lc ) = 1.4 D = 0.05

As, Ds, Es

6 (1+G )∆

50.0

Bs

6 (1+G / 2)∆

70.6

Cs, Fs

6 (1+ 2G )∆

31.6

An, Dn

6 2 − (4G + 1)(G + 1)∆ G + 1

6.7

Bn

12 4 − (4G + 1)(G + 1)∆ G + 1

17.4

Cn

6 2 − (8G + 1)(2G + 1)∆ 2G + 1

10.0

Subassemblages Sway

Nonsway

Remarks: G = (EIb/Lb)/(EIc/Lc), Δ = (ds − dr)/dr


15

where m = M/Mpb, mu = M u M pb , θ = θr θ 0 , θ0 = Mu/Rki. M, Mu, and Mpb are connection moment, ultimate-connection moment capacity, and fully plastic moment of connected beam, respectively. – = 1.0 according to the Equation 1.2 has different shapes as illustrated in Figure 1.13 for m u values of n. As can be seen from Equation 1.2, the connection curve is uniquely determined by three parameters. That is, ultimate-moment capacity Mn, initial stiffness Rki, and shape parameter n. The shape parameter n is determined such that the connection model given by Equation 1.2 best fits the experimental data. In the original classification system by Goto et al. (1998), empirical equations (Kishi and Chen, 1993) based on a statistical analysis of the connection databank by Chen and Kishi (1989) were used in order to estimate the values of n for the respective connection types. This is to reduce the independent parameters of Equation 1.2 to Rki and Mu in view of the simplification in the classification procedure. However, the empirical equations for the estimation of the shape parameter n are considerably approximate and may impair the accuracy of the classification system. Therefore, the boundary moment-rotation curves are herein determined in terms of Rki, Mu, and n, being different from the original classification system (Goto et al., 1998). The boundary values for the initial stiffness Rki between rigid and semi-rigid connections are determined, as shown in Table 1.5, from the behavior of subassemblages at the serviceability limit state. On the other hand, the boundary values for the ultimate-moment capacity Mu and shape parameter n are expressed in terms of interaction equations that are determined by the behavior of subassemblages at the ultimate-limit state. In order to classify the connections to be rigid from the ultimate behavior of frames, EC3 uses the following criterion, which only considers the ultimate strength of the frames: Fur − Fus ≤ 0.05 Fur

(1.3)

where Fur, Fus are ultimate strengths, respectively, of rigid and semi-rigid frames.

m

n= ∞

1.0

n=6

0.5

n=4 n=2

0

0.5

1.0

FIGURE 1.13 Three-parameter power model.

1.5

2.0

mu = 1

2.5

θ

16


The criterion expressed by Equation 1.3, however, may be insufficient because the displacement of frames at the ultimate-limit state is not reflected. Therefore, the following classification criterion is used based on the tolerance Δu, which takes into account both strength and displacement at the ultimate-limit state:  ( F − F )  2  (d − d )  2  ur  us us  ur  (1.4)   +  ≤ ∆u Fur dur     where (Fur, dur) are the coordinate values of the limit point of an equilibrium curve for a rigid subassemblage expressed in terms of force-displacement relation, while (Fus, dus) are the coordinate values nearest to (Fur, dur) of an equilibrium curve for the corresponding semi-rigid subassemblage, as shown in Figure 1.14. It should be noted that (Fus, dus) is not necessarily a limit point of the equilibrium curve for the semi-rigid subassemblage. As the tolerance Δu, the following value is used: ∆ u = (0.05)2 + (0.05)2 ≅ 0.07

(1.5)

Based on the classification criterion for the ultimate behavior of semi-rigid subassemblages given by Equation 1.4 and Equation 1.5, the boundary values between rigid and semi-rigid connections are determined for the ultimate-moment capacity Mu and shape parameter n expressed in terms of interaction equations. The ultimate behaviors of the subassemblages are calculated by geometrically and materially nonlinear analysis with monotonically increasing the vertical displacement at the loading point of compressive column load P (Figure 1.12). In this analysis, the horizontal load H and the vertical load V are ignored. The analysis method used for this calculation precisely considers the geometrical and material nonlinearities in the structural response.

Fs F , r Fur Fur

1.0

0.07

Rigid subassemblage a b c a Subassemblage with connections b classified as rigid

c Subassemblage with connections classified as semi-rigid

0

1.0

d ds , r dur dur

FIGURE 1.14 Equilibrium curves of subassemblages with connections classified as rigid.


17

Furthermore, initial geometrical imperfections as well as residual stresses are taken into account, following the ECCS recommendation (ECCS, 1984). The stress-strain relation used for the respective subassemblages and initial imperfections are shown in Figure 1.15. Extensive numerical analyses are carried out on the twelve types of subassemblages (Figure 1.12) with various member sizes to identify the boundary values for the connection moment – (= M /M ) and shape parameter n, following the criterion given by Equation 1.4 and capacity m u u pb Equation 1.5. In Equation 1.4, Fur and Fus are the ultimate values of P for the respective subassemblages, while dur and dus correspond to the ultimate-vertical displacement at the loading point

− σr = 0.005 L

− σr

+σr

+σr

σr = 0.3 fy L

− σr

L

a b

− σr

+σr +σr

σ Est = 0.02 E

fy

E

E

εy

εst = 10 εy

15 %

−fy c FIGURE 1.15 Imperfections and material properties of subassemblages: (a) initial geometric imperfections; (b) residual stress; (c) stress-strain relation.

ε

2 fy

0.0340

0.0426

0.0329

En

Fn

0.0296

Cn

Dn

0.0340

0.0050

Fs

An

0.0035

Es

Bn

0.0242

−0.2143

Ds

0.0036

−0.0077

0.0101

0.0068

0.0234

0.0101

−0.0015

0.0522

0.0054

−0.0170

0.0263

−0.2933

−0.0321

Bs

Cs

−0.0026

−0.0020

As

c2

c1

Subassemblage

0.1224

0.0327

−0.3594

−1.3965

−0.1281

−0.3594

0.0097

−0.3322

−0.0208

0.0688

0.3465

0.0413

c3

0.4415

0.7482

1.3748

3.4374

1.0543

1.3748

0.9887

1.4543

0.9793

1.0498

1.3991

0.9931

c4

−0.0299

−0.0893

−0.1771

−0.0161

−0.2008

−0.1771

−0.0207

−0.1051

0.0112

−0.0352

−0.2221

−0.0231

c5

0.0703

−0.1739

−1.2436

−2.4585

−1.1667

−1.2436

−0.0196

−0.9124

−0.0470

0.0649

−1.0559

−0.1252

c6

0.0974

0.1159

0.2559

−0.1592

0.3115

0.2559

0.0111

0.1507

0.0112

−0.0242

0.2122

0.0385

c7

−0.0016

0.0018

−0.0002

0.0030

−0.0030

−0.0002

0.0002

−0.0125

−0.0032

0.0081

−0.0041

0.0000

c8

0.2883

0.3105

0.8971

1.5685

0.7797

0.8971

0.0472

0.7557

0.0216

−0.0126

0.5701

0.0554

c9

TABLE 1.6 Coefficients c1 ~ c10 for interaction equations between boundary moment capacity mub and boundary shape parameter nb

−0.0203

−0.0106

−0.0097

−0.0001

−0.0064

−0.0097

−0.0005

0.0754

−0.0095

0.0095

0.0517

−0.0036

c10

18 Semi-rigid Connections Handbook


19

– b = Mb M of P. Based on the numerical data obtained for the boundary moment capacity m u pb u b and boundary shape parameter n , the interaction equations between these two quantities for the respective subassemblages are empirically derived through curve-fitting techniques. All the empirical interaction equations are assumed here to have the following form: n b = c1 + c2 G + c3 λ + c5Gλ + c6 λ mub + c7 Gmub + c8 G 2 + c9 λ 2 + c10 (mub )2 (1.6) m where c1 ~ c10 are curve-fitting coefficients determined by the least square method, according to the types of subassemblages. G and λ that denote relative stiffness and normalized column slenderness ratio, respectively, are expressed by:

G=

(I (I

b c

Lb ) Lc )

L  λ =  c   πr 

,

(1.7a)

fy

(1.7b)

E

where r is the radius of gyration of member cross section; E is Young’s modulus; fy is yield stress of member material. G and λ are introduced to consider the layout and member details of the subassemblages. The values of the curve-fitting coefficients c1 ~ c10 applicable to the following parameter range are summarized in Table 1.6:

0.7 ≤ G ≤ 4.2, 0.2 ≤ λ ≤ 1.0, 0.8 ≤ mu ≤ 1.2

(1.8a-c)

The required rotational capacity θu is defined as the maximum rotation θ max of the connections that is experienced up to the maximum load carrying capacity of the semi-rigid frames (Goto and Miyashita, 1995). The connections classified as rigid generally exhibit smaller rotation than do the connections that have the boundary moment-rotation characteristics between rigid and semi-rigid connections. This implies that the required rotational capacity calculated based on the boundary moment-rotation characteristics between rigid and semi-rigid connections will provide an upper bound that will be safe for the design of connections classified as rigid. Therefore, the required rotational capacities θu for the respective subassemblages are calculated by the nonlinear numerical analyses, assuming that the connection behavior is expressed by the boundary moment-rotation curve between rigid and semi-rigid connection as given by: m = mubθ /(1 + θ n )1/ n n

n

(1.9)

where θ = θr θ 0 and θ0 = M /R . Based on these numerical results, the required rotational capacities θu = θu θ 0 for the respective subassemblages classified as rigid are approximated by the empirical formulas as shown: b u

b ki

θu = d1 + d 2 G + d3 λ + d5Gλ + d6 λ mub + d 7 Gmub + d8 G 2 + d9 λ 2 + d10 (mub )2 (1.10) m where d1 ~ d10 are the curve-fitting coefficients shown in Table 1.7. These coefficients are obtained by the least square method for the range given by Equation 1.8. The validity of the proposed classification system is precisely examined for four types of sway and nonsway frames (Goto et al., 1998).

0.0455

−0.0819

0.0674

−0.0067

−0.0746

−0.0022

−0.0208

−0.0093

−0.0601

−0.0160

−0.0057

−0.1933

Bs

Cs

Ds

Es

Fs

An

Bn

Cn

Dn

En

Fn

0.0147

−0.0058

−0.0489

−0.1395

−0.0359

−0.0489

0.0004

0.0602

0.0062

−0.0280

0.0024

−0.0054

As

d2

d1

Subassemblage

−0.0243

0.0292

0.0883

1.8213

0.1597

0.1193

−0.0345

−0.6142

−0.0204

0.1349

−0.2690

−0.0021

d3

TABLE 1.7 Coefficients d1 ~ d10 for formulas to predict θu

0.6966

1.0029

0.9737

1.7711

1.0099

0.9820

1.0047

1.1700

0.9981

0.9662

1.1447

1.0006

d4

−0.0513

−0.0139

−0.0785

−0.3256

−0.0473

−0.0830

0.0219

0.1798

0.0119

−0.0358

0.0539

0.0070

d5

1.5172

−0.0052

−0.0104

−5.7450

−0.0854

−0.0559

0.0131

0.0040

0.0302

−0.1781

−0.0769

0.0150

d6

0.0828

0.0003

0.0531

0.3240

0.0116

0.0549

−0.0037

−0.0437

−0.0038

0.0348

−0.0034

−0.0009

d7

0.0067

0.0023

0.0153

0.0397

0.0099

0.0156

−0.0007

−0.0171

−0.0017

0.0039

−0.0098

−0.0008

d8

−0.0959

0.0146

0.1319

−0.5660

0.0389

0.1246

−0.0278

−0.0588

−0.0466

0.0860

−0.0001

−0.0294

d9

0.0714

−0.0002

0.0095

−0.0753

−0.0069

0.0076

0.0033

0.0725

0.0065

−0.0336

0.0485

0.0035

d10



21

1.1.7 Comparison of Existing Classification Systems 1.1.7.1 General

Classification of connections is normally made in terms of the index properties such as stiffness, strength, and rotation capacity. Among these index properties, AISC classification (AISC, 2005) adopts only stiffness except for the classification of simple connections where strength requirement is considered in addition to the stiffness. Eurocode 3 (CEN, 2005) adopts both stiffness and strength. The other classification systems (Bjorhovde et al., 1990; Nethercot et al., 1998; Goto et al., 1998) utilize all three indexes. Herein, the respective classification systems are compared with one another in terms of stiffness, strength, and rotation capacity.

1.1.7.2 Classification of Connection Stiffness

The connection stiffness is the most important index in the classification systems. The effect of connection stiffness on the overall behavior of frames is governed by the layout and details of members such as beams and columns. In addition, this effect is different according to whether the frames are sway or nonsway. Normally, the classification based on sway frames tends to yield a more restrictive criterion. Eurocode 3 (CEN, 2005) specifies different classification criteria for initial connection stiffness according to whether the horizontal displacement is restrained or not. However, the model used to derive a classification criterion is a pin-based portal frame (Figure 1.3). Furthermore, nondimensional connection stiffness parameters are simplified to include only the bending rigidity of the connected beam. This implies that the rigidity of the connected column is ignored. AISC specification (AISC, 2005) uses the secant connection stiffness at the service load for classification. A simple beam model with semi-rigid connections at both ends (Figure 1.5) is used to derive the criteria for classification. As a result, this classification system ignores the sway behavior of frames as well as the rigidity of columns. Bjorhovde’s classification criterion (Bjorhovde et al., 1990) that uses the initial stiffness of connections is intended for the case where prior knowledge concerning the member and structural details is unavailable. Therefore, this classification system ignores the overall behavior of frames. Nethercot’s classification system (Nethercot et al., 1998) adopts the initial stiffness of connections as a stiffness index. This classification takes into account the bending rigidities of the connected beam and column. The classification criteria are derived both for serviceability limit state and for ultimatelimit state. These criteria are based on a single-span nonsway subframe under uniformly distributed load applied on the beam, as illustrated in Figure 1.9. This subframe model may be interpreted as a subassemblage of nonsway frames. Although Nethercot considers the bending rigidities of the connected beam and column in the classification, the submodel used to derive the classification are too simple to reflect the actual behavior of frames, being similar to the AISC and EC3 classification. Furthermore, it will be cumbersome to use different connection models in the frame analysis for design, depending on whether the limit state of concern is the ultimate or serviceability limit state. A more detailed classification criterion for the boundary between rigid and semi-rigid connections is proposed by Goto et.al. (1998) in terms of initial connection stiffness. To take into account the behavior of frames in the classification of connections, several subassemblages are used to derive the classification criterion such that the subassemblages will appropriately represent the behavior of the respective parts of the multistory multibay frames with sway or nonsway displacement. As a result, this criterion includes the effect of the bending rigidities of the connected beams and columns.

1.1.7.3 Connection Strength and Rotation Capacity

In AISC specification, the required strength and rotation capacity of connections depend on a particular application. That is, the strength of connections is designed to resist the moment

22


demand under the design load, while the rotational capacity must be larger than the rotational demand of connections at the strength-limit state of frames. Almost similar to AISC specification, connections are designed in EC3 to have a rotational capacity that meets their rotational deformation demand under the design load. The rotational demand has to be calculated by frame analysis except for continuous connections (CEN, 2005) and FR connections (AISC, 2005) that have the strength larger than that of the connected beams. Specifically, in the case of semicontinuous connections (CEN, 2005) and PR connections (AISC, 2005), as well as in the case of FR connections with the partial strength of a connected beam (AISC, 2005), the connection behavior has to be appropriately reflected in the frame analysis. As can be seen from the connection modeling explained above, it will be more appropriate to classify the FR connections with the partial strength of a connected beam (AISC, 2005) as PR connections.

1.2 AISC Specification 1.2.1 Introduction

In the 2005 ANSI/AISC Specification (AISC, 2005), connections are largely classified into two types: Simple and moment connections. A simple connection transmits a negligible moment across the connection. In the analysis of the structure, simple connections may be assumed to allow unrestrained relative rotation between the framing elements being connected. These connections may be modeled as pinned. A moment connection transmits moment across the connection. Two types of moment connections—fully restrained (FR) moment connection and partially restrained (PR) moment connections—are permitted. An FR connection transfers moment with a negligible rotation between the connected members. In the analysis of the structure, the FR connection may be generally assumed to allow no relative rotation and be modeled as rigid. A PR connection transfers moment but the rotation between connected members is not negligible. In the analysis of the structure, the PR connection is modeled as semi-rigid and the momentrotation response characteristics of the PR connection shall be included in the connection model. For simple and FR connections, the connection proportions are established after the final analysis of the structural design is completed. In contrast, the design of PR connections is inherently iterative because the values of connection proportions must be assumed in order to establish the force-deformation characteristics of the connections that are needed to carry out the structural analysis. Herein, the design of semi-rigid connections is explained and discussed based on the commentary of the 2005 ANSI/AISC specification.

1.2.2 Connection Classification 1.2.2.1 General

A connection is a medium through which forces and moments are transmitted from one member to another. A beam-to-column connection is generally subject to axial force, shear force, bending moment, and torsion. Regarding its in-plane behavior, the effect of torsion can be excluded. Furthermore, the effects of axial and shear forces are usually small compared to that of bending moment. Consequently, for practical purposes, only the effect of moment on the rotational deformation needs to be considered regarding the deformation of connections. As depicted in Figure 1.1, the connection rotates by an amount θr when a moment M is applied. The angle θr corresponds to the relative rotation between the beam and the column at the connection. Therefore, in the AISC specification, the in-plane behavior of semi-rigid connection is represented by the M − θr curve, referred to as moment-rotation curve. The moment-rotation curve of a connection is assumed to represent the behavior of a region consisting of the column and beam along with the connecting elements. The primary index properties that govern the moment-rotation charac-


23

teristics of connections adopted in the AISC specification are stiffness, strength, and ductility that will be explained in the next three sections.

1.2.2.2 Connection Stiffness

Most connections exhibit nonlinear behavior at low moment-rotation levels. Therefore, the initial stiffness of a connection Rki inadequately characterizes the connection behavior at service load levels. Furthermore, many connection types do not exhibit a reliable initial stiffness, or they exist only for a small moment-rotation range. The secant stiffness Rks at service loads shown in Figure 1.16 is taken as an index property of connection stiffness for the connection classification. Rks is defined as Ms/θs where Ms and θs are the moment and rotation, respectively, at service loads.

1.2.2.3 Connection Strength

The strength of a connection is the maximum moment Mn in the moment-rotation relation shown in Figure 1.16. The strength of a connection can be determined based on an ultimate-limit-state model of the connection, or from a physical test. If the moment-rotation response does not exhibit a peak load, then the strength can be taken as the moment at a rotation of 0.02 radians.

1.2.2.4 Connection Ductility

The connection ductility (the rotation capacity) θu can be defined as the value of the connection rotation at the point where the resisting strength of connection has dropped to 0.8Mn as shown in Figure 1.16. If the connection does not exhibit a 0.2Mn drop of the resisting moment beyond 0.03

M(θr )

Moment, M

Rki

Rks

Mn

0.20 Mn

Ms

θs

θn

Rotation, θr

θu

FIGURE 1.16 Definition of stiffness, strength, and ductility characteristics of the moment-rotation response for partially restrained connections.

24


radians, the connection ductility θu is taken as 0.03 radians. The latter criterion is intended to apply to connections where there is no significant loss in strength until large rotations occur.

1.2.2.5 Classification Scheme

The AISC classification scheme for simple, FR, and PR connections is summarized in Table 1.4. The classification boundaries are expressed in terms of the nondimentionalized secant connection stiffness RksLb/EIb at service load where Lb and EIb are the length and the bending rigidity, respectively, of the connected beam. This classification is applied to both sway and nonsway frames, being different from the Eurocode3 (CEN 2005) where different classification boundaries are proposed according to whether the frame is braced or unbraced. As for the connection-moment strength Mn, an explicit condition in the classification is imposed only on the simple connections. The connection moment of M ≤ 0.2Mpb at 0.02 radians is considered to have no flexural strength for design. The strengths of FR and PR connections must be adequate to resist the connection moment and shear force demands imposed by the design load. Therefore, it is possible in the AISC specification for an FR connection to have strength less than that of a connected beam. Furthermore, it is also possible for a PR connection to have strength greater than the strength of the beam. The strength requirement for FR connections is not as strict as that for rigid connections in EC3 where rigid connections must always have strength greater than the full strength of the connected beams or columns. However, if the FR connections have marginally higher or partial strength of the connected beam, it is necessary to calculate the rotational demand of the connections under the factored load by using the semi-rigid modeling of connections. Therefore, in view of the simplification of design analysis procedure, it will be of little use to classify connections with marginally higher or partial strength of the connected beam as FR connections. This connection type should be classified as PR. The rotation capacity θu of connections is required to exceed their demands calculated at the strength-limit state of frames. In the absence of an accurate analysis, a rotation capacity θu of 0.03 radians is considered adequate. The above requirement must also be applied to the FR connections with marginally higher or partial strength of the connected beam. However, for the FR connections with strength substantially higher than that of the connected beam, there is no requirement in their rotation capacities. This is because the deformation is controlled by the plastification of the connected beam, and the FR connections exhibit an elastic behavior at the strength-limit state. Figure 1.17 schematically shows the examples of moment-rotation responses of simple, PR, and FR connections classified according to the AISC scheme.

1.2.3 Structural Analysis and Design for Frames with PR Connections

If the connections in a steel framework are classified as either simple or FR, it is allowed to perform the design analysis for the frame assuming that the connections are either ideally pinned or fully rigid. The assumption of fully rigid connection implies that no relative rotation of connection occurs, while the assumption of pinned connection implies that no restraint for rotation of connection exists and the connection moment is always zero. The assumption of the simple or the FR connection simplifies considerably the analysis and design procedures. The proportions of these connections can be established after the final analysis for the structural design is completed. Simple connections are generally designed under the shear force and must meet the required rotation without introducing moment strength and stiffness that may significantly alter the mode of response. On the other hand, FR connections will be designed for the combined effect of forces resulting from moment and shear and must have sufficient stiffness to transmit moment and maintain the original angle between connected members.


FR

Rks =

Mn

Moment, M

Mpb

25

20EIb Lb

M(θr )

θu

θs

Mn

θs

PR

θu θs

Mn 0.03

θu

Rks =

Simple

2EIb Lb

Rotation, θr (radians) FIGURE 1.17 Classification of moment-rotation response of fully restrained (FR), partially restrained (PR), and simple connections.

When PR connections are used, the relevant moment-rotation relation must be included in the analysis of the structure to determine member forces, connection forces, displacements, and frame stability. Therefore, PR construction first requires that the connection moment-rotation characteristics must be known and second, requires that these characteristics be incorporated into the analysis and member design. In contrast to the design of simple and FR connections, it should be noted that the design of PR connections is inherently iterative because the connection proportions must be assumed in order to establish their moment-rotation characteristics that are used in the structural analysis. The PR connections must transfer the moment similar to the FR connections, whereas the PR connections must have the rotational capacities that meet the rotation demands similar to the simple connections. Therefore, the connections have to be designed under the combined effect of moment and shear such that their rotational capacity satisfies the rotational demand at the strength-limit state. Typical moment-rotation curves for many PR connections are available from existing connection databases. When utilizing the databases, care must be taken not to extrapolate data to sizes or conditions beyond those used to develop the database since other failure modes may control. For the connections out of the range of the databases, it may be possible to derive the momentrotation characteristics from tests, component models, or finite element studies. Details of connection databases and connection models are explained in Chapters 4 and 5. Usually, design of PR construction requires separate analyses for the serviceability and strengthlimit states. For the serviceability limit state, an analysis using linear springs with a stiffness given by Rks is sufficient if the resistance demanded of the connection is well below the strength. When

26


subjected to strength load combinations at the ultimate-limit states, a more careful procedure is needed so that the connection characteristics assumed in the analysis are consistent with those of the actual connection response. The response will become nonlinear as the applied moment approaches the connection strength. In particular, the effect of the connection nonlinearity on second-order moment and stability checks need to be considered. The design requirements for simple, PR, and FR connections are shown in Table 1.4.

References AISC, Specification for Structural Steel Buildings, ANSI/AISC 360-05, American Institute of Steel Construction, Chicago, IL, 2005. Bijorhovde, R., Colson, A., and Brozzeti, J., Classification system for beam-to-column connections, Journal of Structural Engineering, ASCE, 116(11), 3059-3076, 1990. CEN, Eurocode 3, Design of Steel Structures, Part 1-1: General rules and rules for buildings, EN 1993-1-1, Part 1-8: Design of joints, EN 1993-1-8, European Committee for Standardization, Brussels, Belgium, 2005. Chen, W. F. and Kishi, N., Semi-rigid steel beam-to-column connections: Data base and modeling, Journal of Structural Engineering, ASCE, 115(7), 105-119, 1989. European Commission for Constructional Steelwork (ECCS), Ultimate-limit state calculation of sway frames with rigid joints, Systems Publication No.33, Technical Working Group 8.2, Brussels, Belgium, 1984. Goto, Y. and Miyashita, S., Classification system for rigid and semi-rigid connections, Journal of Structural Engineering, ASCE, 124(7), 750-757, 1998. Goto, Y. and Miyashita, S., Validity of classification systems of semi-rigid connections, Engineering Structures, 17(8), 544-553, 1995. Horne, M. R. and Merchant, W., The stability of frames, Pergamon Press, 1965. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K. G., Design aid of semi-rigid connections for frame analysis, AISC Engineering Journal, 30(3), 90-107, 1993. Leon, R. T., Composite semi-rigid construction, AISC Engineering Journal, 31(2), 54-67, 1998. Nethercot, D. A., Ahmed, T. Q., and Li, B., Unified classification system for beam-to-column connections, Journal of Constructional Steel Research, 45(1), 39-65, 1998.

2

Effects of Semi-rigid Connections on Structural Members and Frames

Eric M. Lui Meredith Professor, Department of Civil and Environmental Engineering, Syracuse University, NY Zhiling Zhang Graduate Student, Department of Civil and Environmental Engineering, Syracuse University, NY

2.1 Introduction............................................................................................................................. 27 Connection Behavior 2.2 Effects of Semi-rigid Connections on Columns................................................................. 32 Column Effective Length Factor • K Factor for Columns in Semi-rigid Frames 2.3 Effects of Semi-rigid Connections on Beams...................................................................... 40 Lateral Torsional Buckling Load for Compact Beams • Beams with Semi-rigid Connections 2.4 Effects of Semi-rigid Connections on Frames..................................................................... 45 Analysis of Semi-rigid Frames • Design of Semi-rigid Frames • Drift of Semi-rigid Frames 2.5 Summary and Conclusions.................................................................................................... 67

2.1 Introduction A connection is a medium through which forces and moments are transmitted from one member to another. In a conventional analysis and design of steel frameworks, the frames are often conveniently analyzed and designed under the simplifications that the connections behave either as ideally pinned or fully rigid. The use of the ideally pinned condition implies that no moment will be transmitted between the beam and the column. As far as rotation is concerned, the beam and column that are jointed together by a pin will behave independently. On the other extreme, the use of the fully rigid condition implies that no relative rotation will occur between the adjoining members. The angle between the beam and the column remains virtually unchanged as the frame deforms under the applied loads. Although the use of these idealized joint behaviors drastically simplifies the analysis and design procedures, the predicted response of the frame may not be realistic as most connections used in actual practice transmit some moment and experience some deformation. 27

28


According to the American Institute of Steel Construction (AISC, 2005), a connection is considered semi-rigid or partially restrained (PR) if its stiffness Rk falls in the range 2EIb/Lb
2.1.1 Connection Behavior

Although a general set of forces that may be transmitted in a typical beam-to-column connection includes axial force, shearing force, bending moment, and torsion, for simplicity in analysis and design, usually only the effect of in-plane bending moment and the resulting connection rotational deformation is considered. As a result, aside from a few exceptions (Cerfontaine and Jaspart, 2002; Urbonas and Daniunas, 2005, 2006), analytical and experimental work on connections conducted in the past few decades have focused primarily on their flexural response (Frye and Morris, 1976; Lui and Chen, 1987, 1988; Cunningham, 1990). The flexural behavior of connections is best described by their moment-rotation (M-θr ) curves. A connection momentrotation curve relates the beam moment M transmitted by the connection to the in-plane rotational deformation θr experienced by the connection as shown in the inset of Figure 2.1, in which schematic M-θr curves for a variety of commonly-used semi-rigid connections are shown. θr

Moment, M

Column

T-stub

M

Beam

End Plate

Top and Seat Angle

Header Plate

Double Web Angle Single Web Angle Rotation, θr

FIGURE 2.1 Moment rotation behavior of commonly used semi-rigid connections.


29

The single web angle connection represents a flexible connection and the T-stub connection represents a rather stiff connection. Several observations can be made from this figure:

1. All types of connections exhibit M-θr responses that fall between the extreme cases of ideally pinned (the horizontal axis) and fully rigid (the vertical axis) conditions. 2. For the same moment, a larger θr is experienced by a more flexible connection. Conversely, for a specific value of θr, less moment is transmitted by a more flexible connection. 3. The maximum moment that a connection can transmit (herein referred to as the nominal connection moment capacity, Mcn) decreases with the more flexible connection. 4. The M-θr relationships for all semi-rigid connections are typically nonlinear over virtually the entire loading range.

Moment, M

Generally speaking, linear approximation of the initial portion of the curve is acceptable for a frame designed under a serviceability limit state, but becomes unacceptable if the frame is to be designed under a strength limit state. When a moment is applied to a connection, the connection rotates according to the curves shown in Figure 2.1. However, if the direction of moment is reversed, the connection will unload and follow a different path that is almost linear and with a slope more or less equal to the initial slope of the M-θr curve. This phenomenon is depicted in Figure 2.2.

Loads

Unloads

Rotation, θr FIGURE 2.2 Loading and unloading behavior of semi-rigid connections.

30


Because of this behavior, identical connections may not always behave identically. This can best be illustrated by the simple portal frame shown in Figure 2.3. Under the action of the gravity load, the connections at the ends of the beam will experience a moment equal to Mg on the M-θr curve (Figure 2.3a). Now, if a lateral force is applied, the leeward connection will continue to load but the windward connection will unload (Figure 2.3b). As a result, the apparent stiffness of the connections under the action of this lateral force will be different. Depending on the magnitude of Mg and the characteristic of the connection M-θr curve, the difference in stiffness of the two connections may be quite substantial. In the extreme scenario when the gravity load moment equals the nominal moment capacity of the connections, the leeward connection will behave virtually like a pinned connection, whereas the windward connection will respond like a linear elastic connection. This loading and unloading characteristic of the connection must be properly modeled in order to reliably predict the response of the frame. Empirical equations describing the moment-rotation behavior of various connection types have been proposed by a number of researchers using parametric or curve-fitting techniques. A summary of these equations can be found in Chen and Lui (1991), Chen et al. (1996), Chen (2000), and in this handbook. Connection behavior needs to be addressed in terms of stiffness, strength, and rotational ductility. Each of these attributes will be examined briefly in Sections 2.1.1.1 through 2.1.1.3 (ASCE, 1997).


Although almost all connection M-θr curves exhibit nonlinear behavior from practically the onset of loading, it may be desirable for design purposes to employ linear approximations. To account for the loading and unloading behavior of a connection, a minimum of two connection stiffness values need to be identified—the initial stiffness Rki and the ultimate stiffness Rku. For Rki, a somewhat conservative approach is to approximate its value using the secant stiffness obtained as the slope of a line connecting the origin of the M-θr curve to the point Mg, as shown in Figure 2.3a. The value Rku can be taken as the slope of the M-θr curve at Mcn (i.e., the connection stiffness at its nominal moment capacity). Alternatively, Rku can conservatively be taken as zero.

2.1.1.2 Connection Strength

A connection is said to have reached its nominal moment capacity (Mcn) if the moment in the connection is at or near the flat portion of the M-θr curve. Connection strength, however, is only relevant when compared to the strength of the adjoining beam. If we define Mpb as the plastic moment capacity of the beam, a connection is referred to as a full strength connection if Mcn/Mpb ≥ 1.0, and partial strength if otherwise. It is important to note that Mcn obtained from many of the M-θr equations or the connection databases corresponds to only one mode of failure (typically flexural yielding of the connecting elements). Consequently, the equations cannot be used to determine Mcn if other failure modes such as bolt shear, bolt tension, component or weld fractures, etc., control the design. The distinction between partial and full strength connections is important regarding the required ductility. It should be noted that most partially restrained connections are partial strength, resulting in important consequences in design (Leon, 1994).

2.1.1.3 Connection Rotational Ductility

If properly designed, most partial-strength semi-rigid connections exhibit ductile behavior. The inelastic deformation capacity, defined as the ratio of the rotation of the connection at Mcn to the rotation of the connection at Ms (the service load moment) i.e., μ = θcn/θs is often greater than 10 in monotonic tests. However, for full-strength semi-rigid connections, the moment introduced in the joint will be capped by Mpb, resulting in a shift of deformations to the plastic hinge of the

Unloads

θr (b)

Connection Loads

Connection Unloads

FIGURE 2.3 Semi-rigid frame with connections undergoing loading and unloading.

M

(a)

M

Mg

Mg

θr

M

M

θr

Loads

θr

Effects of Semi-rigid Connections on Structural Members and Frames 31

32


adjoining beam. The ductility of the connection is therefore less of a concern than if the semirigid connection is partial strength. For partial-strength semi-rigid connections, the large ductility demands result in both the need for careful detailing of the connections and the need for a simplified check to insure that θcn is not exceeded. It should be remembered that ductility demand is highly dependent on load history. The remarks made herein are meant explicitly for monotonic loading cases and not for stability calculations under large seismic loads. Over the past three decades, extensive studies on the effect of connection flexibility on semirigid frames have been conducted and published in various journals. Some of the work has been summarized in book or monograph form. For example, see Chen and Lui (1991), Chen et al., (1996), Chen (2000), and Faella et al. (2000), among others.

2.2 Effects of Semi-rigid Connections on Columns 2.2.1 Column Effective Length Factor

The pin-ended column often serves as a benchmark to which other columns with different end conditions are referenced. Once the compressive strength or critical load of a pin-ended column is known, the strength of the same column with other end conditions can be obtained by using the effective length factor K, defined as: K=

Pe Pcr

(2.1)

where: Pcr = critical load of the end-restrained column Pe = Euler load of a pin-ended column having the same length as the end-restrained column = π 2 EIc /L2c , where E is the modulus of elasticity, Ic and Lc are the moment of inertia and length of the column, respectively For a perfectly straight elastic column, the critical load can be obtained by writing the differential equation that conforms to the specific end conditions of the column. The eigenvalue of the characteristic equation that corresponds to the differential equation is the critical load for that column (Timoshenko, 1961; Chen and Lui, 1987). The effective length factor can then be determined from Equation 2.1. Table 2.1 shows the theoretical and suggested design K values for six idealized conditions in which joint translation and rotation are assumed either fully realized or nonexistent. A more general case for a perfectly straight column restrained elastically against rotation at ends A and B by rotational springs with spring constants RkA and RkB, and restrained elastically against translation at end B by a translational spring with spring constant Tk, is shown in Figure 2.4. Using the free body diagrams of the column and the rotational springs shown in the figure, the critical load of this column can be found by first writing moment equilibrium equations of the three free bodies and then setting the determinant of the coefficient matrix of the equilibrium equations to zero:

 K1sii + RkA − K 2 (sii + sij ) K1sij  + − K 2 (ssii + sij ) K s K s R 1 ij 1 ii kB det   P  − K 2 (sii + sij ) − K 2 (sii + sij ) 2 K 3 (sii + sij ) − L + Tk  c

   =0   

(2.2)


33

TABLE 2.1 Effective length factors for columns with different boundary conditions Case

Support conditions

Fixed Fixed

Pinned Fixed

Guided Fixed

Pinned Pinned

Free Fixed

Guided Pinned

Theoretical K

0.5

0.7

1.0

1.0

2.0

2.0

Recommended K when idealized conditions are not realized

0.65

0.8

1.2

1.0

2.1

2.0

RkB θB P Tk

Tk RkB

Tk

MBA

P

MBA

B

Tk

θB

Lc

EIc

θA

MAB

RkA

A

P FIGURE 2.4 An end-restrained elastic column.

Tk

MAB

Tk P

RkA θA

Tk

34


where

K1 =

EI c EI EI , K 2 = 2c , K 3 = 3c Lc Lc Lc

sii =

sij =

(2.3)

)

kLc ( sin kLc − kLc cos kLc 2 − 2 cos kLc − kLc cos kLc

(2.4)

)

kLc ( kLc − sin kLc 2 − 2 cos kLc − kLc sin kLc

(2.5)

P EI c

(2.6)

in which k=

The smallest P value that satisfies Equation 2.2 is the critical load for the column of Figure 2.4. The effective length factor can then be obtained from Equation 2.1. Although the effective length factor discussed above was derived from elastic analysis, studies by Chapius and Galambos (1982) and Lui and Chen (1983) have shown that they will be conservative in most cases for initially-crooked elastic-plastic columns provided that the adjoining beams remain elastic. In real structures, a column usually exists as part of a frame. The effective length factor for columns as part of a frame has been derived by Julian and Lawrence (1959) and LeMessurier (1972). By assuming that (1) the girders are rigidly connected to the columns, (2) all columns of a story buckle simultaneously, and at the onset of buckling the rotations of the ends of the girders are equal and opposite for braced frames and equal in magnitude and direction for unbraced frames, and (3) all members are prismatic and the behavior is elastic, the following equations for the effective length factor can be written. For braced (or sway prevented) frames:

)

2  G + GB   G A GB  π  π K  2 tan (π 2 K + A =1 1 − +    π K 4 K 2    tan (π K  For unbraced (or sway permitted) frames:

)

G A GB (π K

)

2

6 ( G A + GB

− 36 −

)

π K =0 tan (π K )

(2.7)

(2.8)

where GA and GB are the stiffness distribution factors at the Ath and Bth ends of the column respectively. They are defined as:

G=

∑ τ ( I L ) ∑ (I L)

c

(2.9)

b

where the subscripts c and b refer to the columns and beams, respectively, and τ is a factor to account for inelasticity in the column given by AISC (2005) as:

 P if ≤ 0.5 1.0 Py  τ =  4 P (1 − P ) if P > 0.5 Py Py  Py

(2.10)


35

where P is the axial force in the column and Py is the yield load of the cross-section. The summation in the numerator covers all columns that come together at a joint and the summation in the denominator covers all beams that come together at the same joint. If the column is supported on a pinned support, the theoretical G factor evaluated using Equation 2.9 at the supported end is infinity. However, recognizing that an ideally pinned support does not exist in real structures, a G factor of 10 is recommended for use. On the other hand, if the column is fixed at the base, the theoretical G factor is 0. Again, because an ideally fixed support does not exist, a G factor of 1 is recommended for use. Equations 2.7 and 2.8 form the bases for the alignment charts shown in Figure 2.5 that are used extensively by designers in the United States.

2.2.2 K Factor for Columns in Semi-rigid Frames

In using the alignment charts of Figures 2.5a and 2.5b to determine column effective length factors, one must first compute the column end restraint parameters GA and GB using Equation 2.9, which assume the beams are rigidly connected to the column in question. If the effect of connection flexibility is to be accounted for, these G factors need to be modified as follows for sway prevented and sway permitted semi-rigid frames.

2.2.2.1 Sway-prevented Frames

For the sway prevented frame, an assumption commonly used is that the restraining beams bend in single curvature with the near end and far end rotations equal but opposite. As a result, the effect of connection flexibility can be incorporated into the G factor computation by replacing the

GA 50.0 10.0 5.0 4.0 3.0 2.0

∞

K

GB 1.0 0.9

∞

GA ∞ 100.0 50.0 30.0 20.0

50.0 10.0 5.0 3.0 2.0

10.0 8.0 7.0 6.0 5.0

0.8 1.0 0.8 0.7 0.6 0.5

0.7

0.6

a

20.0 10.0 5.0 4.0 3.0

2.0

2.0 1.0

0.2

∞ 100.0 50.0 30.0 20.0 10.0 8.0 7.0 6.0 5.0 4.0 3.0 2.0

1.5 1.0

0.1

0.1

0

3.0

0.3

0.3

∞

GB

4.0

0.4

0.4

0.2

1.0 0.8 0.7 0.6 0.5

K

0.5

0

0

1.0

b

FIGURE 2.5 Alignment charts: (a) sway-prevented (braced) frame; (b) sway-permitted (unbraced) frame.

0

36


beam moment of inertia I in the denominator of Equation 2.9 by a modified value I (Lui, 1995, 1996) given by:   1 I ' = 3I  (2.11)   2  1 + 3  − dM F    Rk  dM N  where Rk = Rk L EI , in which I and L are the moment of inertia and length of the adjoining beam, and dMF /dMN is the ratio of the incremental far end to near end connection moments. Because connections at the opposite end of the adjoining beam in a sway-prevented frame normally undergo either loading or unloading simultaneously at incipient instability, one can circumvent the difficulty of having to determine the instantaneous stiffness and the incremental end moments of the loading connections simply by assuming that these connections have zero stiffness. Therefore, only the stiffness of the unloading connections warrants consideration. With this assumption, one can conservatively use:

A. If both the near and far end connections unload:

  1 (2.12) I'= I   1 + 2     Rki   where Rki = Rki L EI , Rki being the initial connection stiffness (see Section 2.1.1.1) B. If both the near and far end connections load, I = 0

If we substitute I = I = 0 into Equation 2.9, we obtain GA = GB = ∞, giving K = 1. This condition represents the most severe case for the column in a sway-prevented frame. For simplicity and conservativeness, an effective length factor of unity can always be used for the design of swayprevented columns.

2.2.2.2 Sway-permitted Frames

An assumption used in developing the alignment chart for the sway-permitted frame subassemblage is that the restraining beams bend in reverse curvature, with the near-end and far-end rotations being equal. With this in mind, one approach to account for the effect of connection flexibility is to replace I in the denominator of Equation 2.9 by I (Lui, 1995, 1996) given by:   1 (2.13) I'= I      dM 3 F 2 1+  −   Rk   dM N   where the definition of Rk and dMF /dMN are the same as for Equation 2.11. However, it should be noted that in applying the above equation, I can be positive as well as negative. A positive I means the beam is imposing restraint on the adjoining column; a negative I means the beam is destabilizing the adjoining column at incipient instability. If I is negative, the corresponding G factor will also be negative. Negative G factor is theoretically possible, but beyond the range of the alignment chart shown in Figure 2.5. If negative G factors are encountered, K must be obtained directly by solving Equation 2.8. It is important to note that for sway permitted semi-rigid frames, the values of dMF /dMN will rarely equal one (i.e., the value assumed in the development of the effective length alignment charts). This is because in most cases, a connection at one end of the beam will tend to load while


37

another connection at the other end of the beam will tend to unload at incipient side-sway instability of the structure. In general, accurate values for Rk and dMF /dMN needed for Equation 2.13 are not readily obtainable. Nevertheless, we will discuss three possible approaches for determining these values. In decreasing order of sophistication, they are:

1. Perform an advanced second-order inelastic analysis and obtain Rk and dMF /dMN directly. This analysis must include all the significant connection and member nonlinearities. Of course, if one performs such an analysis, the analysis in itself would be verification of the structure’s stability, and the application of Equation 2.13 would be unnecessary. Therefore, this procedure is only useful for assessing the ability of Equation 2.13 to predict a frame’s stability behavior, given “exact” values for the relevant parameters. 2. Use approximate values for Rk from simplified bilinear or trilinear M-θr curves. In this approach, one may assume that the stiffness of the loading connection is equal to Rku, and that of the unloading connection is equal to Rki. 3. Employ a simplified behavioral model in which the connection stiffness and incremental moment are assumed to be zero for all loading connections, and Rki is used for all unloading connections. It should be noted that unless the connections have reached their nominal moment capacities under gravity loads acting on the beam, this approach often leads to an overly conservative design. However, the advantage of applying this approach is that only two connection parameters—Rki and Mcn—need to be known, and analytical expressions for these two parameters are available in the literature (for example, Kishi and Chen, 1990; Chen and Lui, 1991; Kishi et al.,1993a, 1993b, 1994).

Because of the ease with which the third approach can be applied to semi-rigid frame analysis, the rest of this chapter presupposes its use. Therefore, the equations that follow are predicated on the assumptions of the third approach. For this situation, the modified beam moment of inertia I becomes: A. If the near end connection unloads and the far end connection loads:   1 I'= I    2 1+ 3    Rk   where Rk = RkiL/EI, Rki being the initial connection stiffness (see Section 2.1.1.1). B. If the near end connection loads and the far end connection unloads, I = 0.

(2.14)

For the special case when the connection stiffness are the same at both ends of the beam (i.e., RkA = RkB), dMF /dMN most likely would be equal to unity (e.g., the connections are identical on each end of the beam, and the total moments MF and MN are the same at each of the ends). Upon substituting dMF /dMN = 1 into Equation 2.13, one obtains:

 1 I'= I 6 1 + Rk 

   

(2.15)

However, it should be noted that the condition RkA = RkB is seldom realized because of the loading or unloading characteristic of the connections. Equation 2.13 is a more general equation, and thus it is more appropriate for use in computing effective length factors for columns in semi-rigid frames.

38


2.2.2.3 Procedure for Evaluating K Using the Modified Moment of Inertia Approach

The steps for employing the modified moment of inertia approach for determining effective length factors for columns in semi-rigid frames are as follows:

1. Calculate the modified moment of inertia I for the beam with semi-rigid connections. 2. Replace I with I and calculate G factors using Equation 2.9. 3. Use the appropriate alignment chart in Figure 2.5a or 2.5b to obtain a nomograph effective length factor K for the column. 4. Modify the K values obtained in Steps 1-3 for the non-leaning columns using the following equation for sway permitted frames where leaning columns are present: K=

∑P all

P

tI c

∑

non − leaning columns

tI c

(2.16)

K2

In Equation 2.16, τ is given by Equation 2.10, P and Ic are the column axial force and moment of inertia, respectively, and ΣP is the sum of the axial force for all columns in a story, including both the leaning and non-leaning columns. Leaning columns are columns that are pinned at both ends. They carry gravity loads, but do not contribute to the lateral stability of the frame. They are to be designed for K = 1. If leaning columns are present in the story, the K values must be calculated only for the non-leaning columns. Non-leaning columns are columns that can provide lateral stability to the frame. All columns that have a predictable amount of rotational end restraint are classified as non-leaning columns.

2.2.2.4 Other Approaches for K Factor Computation

Another approach (Lui, 1992, 1995) to evaluate K for columns in a sway-permitted semi-rigid frame is to perform a first-order analysis on the frame modeled as rigid with the following provisions:

1. Replace I with I computed from Equation 2.13 for all beams with semi-rigid connections. 2. Apply a set of fictitious lateral load ΣH equals to 0.001ΣPu at each story, where ΣPu is the sum of all factored gravity loads acting on that story. 3. Determine the interstory lateral deflection Δ0 due to ΣH. 4. Evaluate the effective length factor of the column using the equation:  π 2 EtI c    Pu   ∆0   1 K=  +   ∑  2   η ∑ H    Pu Lc    all Lc   5 ∑  non −leaning columns  

(2.17)

where η is a member stiffness index given by:

2   M   Eτ I M  η = 3 + 4.8  1  + 4.2  1   3 c   M2   M 2   Lc

(2.18)

in which M1/M2 is the ratio of the smaller to larger end moment of the column. The other terms in Equation 2.17 and Equation 2.18 are defined as before. Other approaches used to evaluate K factor for columns in semi-rigid frames are given by Aristizabal-Ochoa (1994, 1997) and Xu and Liu (2002).


39

Regardless of the approach used, it should be noted that unless Rk is small or G is large, K is not particularly sensitive to changes in the connection stiffness; and when Rk is increased beyond 20, little change in K will occur (ASCE, 1997). This means the uncertainties that are often associated with determining connection stiffness will not have a significant influence on the computed K values.

2.2.2.5 Column Strength Design Equations

Once the effective length factor K is computed, the nominal column strength Pn can be evaluated using the following AISC (2005) equations: For

KL r

≤ 4.71

E fy

:

For

KL r

> 4.71

E fy

fy   F Pn =  0.658 e  f y Ag  

(2.19a)

Pn = 0.877 Fe Ag

(2.19b)

:

where KL is the effective length, r is the radius of gyration, E is the modulus of elasticity, fy is the material yield stress, Ag is the gross cross-sectional area, and: π2 E Fe = 2  KL   r 

(2.20)

Example: For the semi-rigid portal frame shown in Figure 2.6, knowing Rk = Rk L EI = 10 for the connections at B and C, determine the elastic K factor for column AB if: A = The loading or unloading behavior of the connections is ignored. B = The loading or unloading behavior of the connections is taken into consideration. P

P C

B

EI = Constant Length of all members = L

A FIGURE 2.6 Example: K-factor calculation.

D

40


A. If the loading or unloading behavior of the connections is ignored, both connections B and C will have identical stiffness that is equal to 10EI/L. Using Equation 2.13 with dMF /dMN = 1 and Rk = 10, we obtain: I ' =

I 1.6

and from Equation 2.9 with τ = 1, we obtain GA = ∞ and GB = 1.6. Note that the theoretical rather than the recommended GA value of 10 is used in this example so the result can be directly compared with the theoretical solution. From the alignment chart of Figure 2.5b, K for column AB is determined to be 2.5. This calculated value of K compares favorably with the theoretical K value of 2.52 (Lui and Chen, 1988). B. If the loading or unloading behavior of the connections is considered, the connection stiffness for connection B and connection C will be different. If we conservatively assume a connection hinge has formed at C, the stiffness Rk for connection B (which undergoes unloading) will be 10EI/L, but Rk for connection C is now zero, making column CD a leaning column. Using Equation 2.13 with dMF/dMN=0 and Rk = 10, we obtain: I I ' =, 2.6

and from Equation 2.9 with τ = 1, we obtain GA = ∞ and GB = 2.6. Again, the theoretical rather the recommended GA value of 10 is used so the result can be compared with the theoretical solution directly. From the alignment chart of Figure 2.5b, K is determined to be 2.8. However, because of the presence of the leaning column CD, further modification to K is necessary. Using Equation 2.16 with τ = 1 and recognizing that column AB is the only non-leaning column of the frame, we obtain:

K=

2P I = 3.96 P  I   2.82 

The theoretical K value for column AB obtained from a system buckling analysis is 3.93. Thus, good agreement is obtained. In reality, the stiffness for connection C when it is undergoing loading will fall between 0 and 10EI/L, giving an incremental moment ratio dMF /dMN in the range of 0 and 1. The actual K value for column AB will lie anywhere between 2.52 and 3.93. K = 3.93 is thus a conservative estimate of the effective length factor for the column.

2.3 Effects of Semi-rigid Connections on Beams For design purposes, beam cross-sections are classified into compact sections, noncompact sections, and slender compression elements. A compact section is a section that is capable of developing the cross-section plastic moment capacity and sustaining a large rotation at the plastic moment. A noncompact section is a section that may or may not develop the plastic moment capacity. Even if the plastic moment capacity is developed, a noncompact section normally can-


41

not sustain a large rotation at the plastic moment because of, but not limited to, local buckling. A slender compression element is a cross-section component that is susceptible to local buckling under a compressive force. The bending capacity of a compact beam depends on its laterally unbraced length, the axis of bending, the type and pattern of the applied loads, and the support conditions. If the beam is short or adequately braced when bent about its strong axis or if it is bent about its weak axis, the bending capacity will be equal to the plastic moment capacity of the cross-section. On the other hand, if a slender beam without adequate lateral brace is bent about its strong axis, the bending capacity will be controlled by the elastic critical lateral torsional buckling strength. When an intermediate length beam is bending about its strong axis, the bending capacity will be governed by the inelastic lateral torsional buckling strength. As for the type and pattern of the applied loads, the most severe load case is one in which the beam is subjected to a pair of equal and opposite moments. This is because under this load condition, the internal bending moment along the entire length of the beam is a constant and equal to the applied end moments. Finally, as for the support conditions, the more rotational restraint the support provides to the beam, the less susceptible the beam will be to lateral torsional instability.

2.3.1 Lateral Torsional Buckling Load for Compact Beams

When an ideal I-beam is loaded in the plane of the web, in-plane deformation (i.e., bending about the strong axis) will occur at the commencement of the load and increases as the applied force increases. As the magnitude of the load approaches a certain critical value, out-of-plane deformation (i.e., bending about the weak axis) and twisting (i.e., rotational about the longitudinal axis) of the beam will increase rapidly and the beam is said to have reached an unstable state. This critical load is referred to as the lateral torsional buckling load of the beam. It is obtained as the eigenvalue of the bifurcation problem of the beam (Timoshenko, 1961; Chen and Lui, 1987). The theoretical critical moment that corresponds to the elastic lateral torsional buckling of a beam for various support and loading conditions is given by Johnson (1976):

M cr = C1

π 2 EI y

( KL )

2

 C g + C j + 3  2 

(C g + C j ) 2

3

2

C + w Iy

 GJ ( KL 22   1 +   π 2 ECw    

)

(2.21)

where Cw = warping constant E = modulus of elasticity g = distance from shear center to the point of application of the transverse load, taken positive when the load is below the shear center Iy = moment of inertia about weak or y-axis j = S + 21I ∫ y( x 2 + y 2 )dA, , in which S is the distance from the centroid of the cross secx A tion to the shear center, and Ix is the moment of inertia about the strong or x-axis J = torsional constant K = effective length factor for the beam C1, C2, C3 = coefficients which are functions of loading and support conditions (Johnston, 1976) Beams used in practice usually fail at loads below Mcr due to the presence of geometrical and material imperfections. For such beams, lateral deformation and twist commence at the start of loading and increase as the magnitude of the loads increases. The maximum load, referred to as the ultimate load, is obtained as the peak point of the load-deflection curve.

42


To obtain this ultimate load, a load-deflection approach must be used and recourse to numerical analysis is inevitable. Analytical and experimental studies to determine the ultimate loads of beams are available in the literature (for example, Galambos, 1963; Yoshida and Imoto, 1973; Vinnakota, 1977; Yura et al., 1978; Fukumoto et al., 1980; Fukumoto and Itoh, 1981; Trahair, 1993). In general, the presence of residual stresses and geometric imperfections will decrease the nominal strength of the beam. The effect of residual stresses is to cause early yielding, and depending on the types of loadings and residual stress distributions, the nominal strength will be affected differently. The effect of geometrical imperfections is to aggravate the deformation, and so the beam will reach an unstable state at a lower load. Evidently, this effect is more pronounced for slender beams.

2.3.1.1 Beam Strength Design Equations

Based on a semi-empirical approach that takes into consideration geometrical and material nonlinearities, AISC (2005) recommends the use of the following equations to calculate the nominal flexural strength of compact I-shaped beams with lateral unbraced length of Lb bent about the strong axis. For Lb ≤ Lp: M n = M pb = fy Z x

(2.22)

  Lb − L p   M n = Cb  M p − ( M p − 0.7 f y S x )    ≤ M pb   Lr − L p  

(2.23)

For Lp < Lb ≤ Lr: For Lb > Lr:

M n = Cb S x

π 2E  Lb  r   ts 

2

2

J  Lb  1 + 0.078 ≤ M pb S x ho  rts 

(2.24)

The various terms in the above equations are defined as: L p = 1.76 ry

E Lr = 1.95rts 0.7 f y

E fy

 0.7 f y S x ho  J 1 + 1 + 6.76  S x ho J   E

(2.25) 2

(2.26)

where rts2 =

I yCw Sx

, ho = d − t f

(2.27)

in which Cw is the warping constant, E is the modulus of elasticity, fy is the material yield stress, J is the torsional constant, Mpb is the plastic moment capacity of the beam, ry is the radius of gyration about the weak axis, Sx is the elastic section modulus about the strong axis, Zx is the plastic section modulus about the strong axis, and Cb is a factor to account for the type and pattern of the applied loads on the beam. It is expressed as:

Cb =

12.5 M max ≤ 3.0 2.5 M max + 3 M A + 4 M B + 3 M C

(2.28)


43

in which Mmax, MA, MB and MC are the absolute value of the maximum, quarter-point, midpoint, and three-quarter point moments in the unbraced segment of the beam, respectively. Note that the above formulae are applicable only to compact I-shaped sections bent about the strong axis in which lateral torsional instability is the limit state. If the same section is bent about the weak axis, the nominal flexural strength will be the plastic moment capacity about the weak axis.

2.3.2 Beams with Semi-rigid Connections

Like columns, the support conditions of a beam will have an effect on its flexural capacity. Beams that are simply-supported at the ends will have a lower nominal strength than beams that are rigidly supported. In the next two sections, the effect of semi-rigid support condition on beams will be discussed.

2.3.2.1 Analysis of Semi-rigid Beams

For beams with semi-rigid connections, most of the analyses have been focused on using computer-based techniques. However, the analysis of beams with semi-rigid connections can be carried out as rigidly connected beams with the appropriate connection modeling (Cunningham, 1990; Geschwindner, 1991; Chikho and Kirby, 1995). The theory and analysis procedures are discussed by Xu in Chen (2000). The effects of connection flexibility are modeled using rotational springs having stiffness Rk at the ends of the beam. To reflect the relative stiffness of the beam and the rotational end-spring connections, an end-fixity factor is used (Monforton and Wu, 1963; Chen, 2000). It is defined as:

η=

α = φ

1 1+

3 Rk

(2.29)

where α is the member end rotation, f is the combined rotation of the member and the connection due to a unit end moment (see Figure 2.7), Rk = Rk Lb EI b is defined as before in Equation 2.11. Note that η falls between zero and one, and it defines the stiffness of each end connection relative to the adjoining beam. Upon the introduction of the end-fixity factor η to account for semi-rigid behavior, the analysis of semi-rigid beams can be made through minor modification of the conventional moment distribution method for rigidly connected beams. The steps are outlined in items 1–4:

1. Evaluate end-fixity factors ηi and ηj according to Equation 2.29 at the ith and jth ends of the beam with semi-rigid connections.

φ

Rk

α EIb Lb

FIGURE 2.7 A beam restrained by a semi-rigid connection.

44


2. Calculate member stiffness factors Kij and Kji for each semi-rigid beam and obtain moment distribution factor DFij using the following equations:

 12ηi  EI b K ij =    4 − ηi η j  Lb

(2.30)

 12η j  EI b K ji =    4 − ηi η j  Lb

(2.31)

DFij =

K ij

∑K

(2.32) ij

3. Compute the end reaction moments Mij and Mji. 4. Sum the member end moments at each joint to determine the unbalanced moment, and complete the rest of the analysis by conventional moment distribution method for rigid continuous beams.

2.3.2.2 Design of Semi-rigid Beams

For I-beams, the theoretical critical moment that corresponds to the elastic lateral torsional buckling load is given by Equation 2.21. If pinned supports are used at both ends of the beam and a loading consists of a pair of equal and opposite moments are applied to the beam ends, Equation 2.21 can be reduced to: M cr =

π Lb

1+ EI y GJ

π 2 ECw Lb2 GJ

(2.33)

By performing a series of second-order inelastic analyses using different values for Rk and Lb, an empirical equation that can be used for estimating the lateral torsional buckling load of a simply supported I-beam with in-plane semi-rigid connections having connection stiffness in the range 0 < R k < 20 is given by: 3.56 × 10 5 R k M n = M cr + Lb1.32

(2.34)

In the above equation, Mcr is given by Equation 2.33, Lb is the length of the beam in inches (1 inch = 2.54 cm), and R k = Rk Lb EI y , in which Rk is the connection stiffness, and Iy is the moment of inertial of the beam about its weak axis. Note the increase in Mn when R k increases or when Lb decreases. In the event that the applied loads are something other than a pair of equal and opposite moments, Equation 2.34 needs to be multiplied by Cb given in Equation 2.28. Example: Consider the I-beam shown in Figure 2.8. If the beam span Lb is 30 feet (or 360 inches or 9.1 m) and the connections at A and B are semi-rigid connections with an in-plane rotational stiffness of 10EIy /Lb, determine the nominal moment capacity of the beam. The section properties are: Iy = 42.6 in4 (1.77 × 103 cm4), J = 0.769 in4 (32 cm4), Cw = 619 in6 (1.66 × 105 cm6). The material properties are: E = 29,000 ksi (200 MPa), G = 11,200 ksi (77.2 MPa). Using Equations 2.33 and 2.34, Mn is obtained as:

M n = 970 +

3.56 × 10 5 (10 360

1.32

) = 2470 kip-in

(279 kN-m) )


M

Rk

45

Rk

M

Lb FIGURE 2.8 Analysis of semi-rigid beam.

This value is within 5 percent of Mn = 2580 kip-in (291 kN-m) obtained from a second-order inelastic finite element analysis of the beam.

2.4 Effects of Semi-rigid Connections on Frames Semi-rigid frames are frames for which the connections joining the beams and columns are neither fully rigid nor perfectly pinned. In reality, all steel frames are semi-rigid in nature as all connections exhibit a certain degree of flexibility under loads. According to AISC (2005), the effect of semi-rigidity needs to be considered when the connection stiffness Rk, compared to the in-plane bending stiffness EIb/Lb of the beam, falls in the range 2 < Rk Lb / EI b < 20 . The incorporation of connection flexibility into frame analysis normally entails an iterative-type solution process. This is because most connections exhibit nonlinear response almost from the start of loading. The nonlinear behavior of connections is attributed to a number of factors such as local yielding, local buckling, stress concentration, strain hardening, and bolt slip, etc. Some commonly used connection models have been discussed in this handbook. The selection of the proper model for a specific type of analysis depends on the nature of that analysis. In certain situations, it is possible to model the connections as linear elements with constant stiffness. For instance in a bifurcation analysis, we are interested in locating adjacent equilibrium configurations in the immediate neighborhood of the perfect one. As a result, only the initial stiffness property that corresponds to the instantaneous deformation of the structure is of interest. It is therefore reasonable to model the connections as linear elements since only the initial stiffness of the connections is needed for such analysis. The assumption of linear connection behavior is also acceptable in a serviceability analysis. In the analysis of a structure for serviceability, the usual premise is that deformation is small. For small deformation, the nonlinear behavior of most connections is not significant and so the use of a linear model is justifiable. However, in a strength analysis it is important to use a proper nonlinear connection model. Over the past decades, a large number of studies have been conducted and published on the influence of connection flexibility on frame responses (for example, Chen and Lui, 1987; Lui and Chen, 1987, 1988; Lui, 1988; Yau and Chan, 1994; Rodrigues et al., 1998; Aristizabal-Ochoa, 2001; van Keulen et al., 2003; Gizejowski et al., 2004; Sekulovic and Nefovska-Danilovic, 2004). In this section, several general approaches by which connection flexibility can be accounted for in frame analysis will be presented. This is followed by a discussion on the design of semi-rigid frames.

2.4.1 Analysis of Semi-rigid Frames

Nonlinearities in flexibly connected frames consist of three types: (1) the nonlinear M-θr relationship of the connection, (2) the geometrical nonlinearity of the member (P-δ effect) and of the frame (P-Δ effect), and (3) the material nonlinearity or yielding in the members of the frame.

46


Thus, depending on the types of nonlinearity and the degree of accuracy required, three different analysis techniques can be employed (Chen and Lui, 1991).

2.4.1.1 Elastic Bifurcation Analysis of Semi-rigid Frames

In a bifurcation or an eigenvalue analysis of semi-rigid frames, the load that corresponds to a state of equilibrium bifurcation of the frame is sought. This load, referred to as the critical load, is the theoretical maximum load that the semi-rigid frame can sustain. To evaluate this critical load, it is necessary to write the equations of equilibrium of the frame with respect to this deformed configuration taking into account the effect of connection flexibility as described below. 2.4.1.1.1 Beam Stiffness Relationship Consider a beam element subjected to end moments (MA, MB) and an axial force (P) with connections, modeled as rotational springs, attached at both ends as shown in Figure 2.9. Because we are only concerned with the instantaneous deformation of the frame in an eigenvalue analysis, it is justifiable to consider only the initial stiffness of the connection. Denoting RkiA and RkiB as the initial connection stiffness of connections A and B, respectively, the relative rotation between the joint and the beam end (i.e., rotational deformation of the connection) can be expressed as:

θrA =

MA P

θA

θrA

MA M , θrB = B RkiA RkiB

(2.35)

EIb = Constant

A Lb

B θrB

MB P

θB

FIGURE 2.9 Beam element with semi-rigid connections.

If we denote θA and θB as the joint rotations at the Ath and Bth ends of the beam, respectively, the slope-deflection equations for the beam modified for the presence of connections can be expressed as:

MA =

 EI b   M  M   sii  θ A − A  + sij  θ B − B   Lb   RkiA  RkiB   

(2.36a)

MA =

EI b Lb

(2.36b)

   M  M   sij  θ A − A  + s jj  θ B − B   RkiA  RkiB     

where EIb is flexural rigidity and Lb is the length of the beam. sii and sij are stability functions, which for a tensile axial force, are given by:

( kLb )2 cosh kLb − kLb sinh kLb 2 − 2 cosh kLb + kLb si b inh2 kL kLb sinh kLb − ( kLb ) sij = s ji = 2 − 2 cosh kLb + kLb sinh kLb

sii = s jj =

(2.37a) (2.37b)


47

and for a compressive axial force, are given by:

sii = s jj =

sij = s ji =

kLb sin kLb − ( kL )2 cos kLb 2 − 2 cos kLb − kLb sin kLb

(2.38a)

( kLb )2 − kLb sin kLb 2 − 2 cos kLb − kLb sin kLb

(2.38b)

in which k is defined in Equation 2.6. Solving Equations 2.36a and 2.36b for MA and MB gives:

EI b *  s θ + s*θ  Lb  ii A ij B  EI M B = b  s *jiθ A + s*jjθ B  Lb MA =

(2.39a) (2.39b)

where

2  EI b sij2    sij2  EI s 2 EI s   EI s   EI   (2.40a) sii* =  sii + b ii −  /   1 + b ii   1 + b ii  −  b  Lb RkiB Lb RkiB    Lb RkiA   Lb RkiB   Lb  RkiA RkiB     2 2 2 2    EI b sij sij   EI s EI s   EI s   EI   (2.40b) s*jj =  sii + b ii −  /   1 + b ii   1 + b ii  −  b  Lb RkiA Lb RkiA    Lb RkiA   Lb RkiB   Lb  RkiA RkiB     2  sij2  EI b sii   EI b sii   EI b  * *  . (2.40c) sij = s ji = sij /  1 + 1+ − Lb RkiA   Lb RkiB   Lb  RkiA RkiB     Equations 2.39a and 2.39b can be transformed into a member stiffness relationship of a six degree-of-freedom plane frame member shown in Figure 2.10 by relating the member end forces ri, i = 1 to 6, to the member basic forces P, MA, and MB as:

         

 1 0 r1   1   r2   0 Lb   r3   0 1 = r4   −1 0   r5   0 − 1   Lb r6   0  0

     P 0  M A  0    MB 1  − Lb   1  0 1 Lb

    

 0   P∆  Lb  0 +  0  P∆  − Lb    0

           

(2.41)

where (Δ is the relative joint translation of the member. r5, d5 r2, d2

EIb = Constant

r1, d1 r3, d3

FIGURE 2.10 2-D beam element.

Lb

r6, d6 r4, d4

48


Similarly, the member basic displacements u, θA, and θB, where u is the axial deformation of the member, and the member end displacements di, i = 1 to 6, can be related by:

 u     θA   θ   B 

 1   0 =    0 

0 1 Lb

0 −1 1

1 Lb

0

0 0

  0   0     1   

0 1 − Lb −

1 Lb

d1   d2   d3  d4   d5   d6 

(2.42)

Equations 2.41 and 2.42 can be combined by realizing that the basic force-displacement relationship is given by:  P  M A   M B 

    EI b  = L  b     

A 0 Ib 0 sii* 0

s*ji

 0  u    *   θA  sij   θ   B  s*jj  

(2.43)

Upon substitution of Equation 2.42 into Equation 2.43, and then into Equation 2.41, we obtain:  A   Ib    r1    r   2     r3  EI b  =  r  L  b  4    r5    r   6     

0

(s

* ii

0

)

+ 2sij* + s*jj − ( kLb Lb2

) (s 2

* ii

+ sij*

Lb

−

)

sii*

A Ib 0

0

(

sym.

)

− sii* + 2sij* + s*jj + ( kLb

(

Lb2

− sii* + sij*

0 A Ib

0

Lb

)

2

(s

* ij

)

* ii

L

)

0

)

+ 2sij* + s*jj − ( kLb 2 b

Lb sij*

0

(s

+ s*jj

)

2

(

− sij* + s*jj Lb s*jj

)

                  

d1 d2 d3 d4 d5 d6

(2.44)

Symbolically, Equation 2.44 can be written as:

r = k beam d

(2.45)

If the axial force in the beam is small, the beam stiffness matrix kbeam in Equation 2.45 can be simplified by setting sii = sjj = 4 and sij = sji = 2 in Equation 2.40a-c, and with k = ( P EI b = 0 , we have:

)

       


k beam

 A   Ib      EI b   = Lb         

0

(s

* ii

+ 2sij* + s*jj L

0

2 b

) (s

* ii

+ sij* s L

)

A Ib

−

0

b

0

(

* ii

− s

0

* ii*

s

A Ib

−

+2

(

0 * ij

s2 b

+

L sii* + sij* Lb

s

* jj

) (

* ij

+

s

L

)

(s

+ 2sij* + s*jj L L

2 b

b

s

* jj

)

sij*

0 ii*

sym.

49

0

)

(

* ij

+

− s

L * s

where

jj

b

s

* jj

)

          (2.46)         

2  12 EI b    4 EI b   4 EI b   EI b  4    s = 4 + − 1 +  / 1 + Lb RkiB    Lb RkiA   Lb RkiB   Lb  RkiA RkiB    

(2.47a)

2  12 EI b    4 EI b   4 EI b   EI b  4    s = 4 + − 1 +  / 1 + Lb RkiA    Lb RkiA   Lb RkiB   Lb  RkiA RkiB    

(2.47b)

2  4 EI b   4 EI b   EI b  4   sij* = s*ji = 2 /   1 + − + 1      Lb RkiA   Lb RkiB   Lb  RkiA RkiB    

(2.47c)

* ii

* jj

2.4.1.1.2 Column Stiffness Relationship Referring to Figure 2.11, the force-displacement relationship of the column taking into account the geometrical nonlinear effects in the absence of in-span loadings can be expressed symbolically as (Chen and Lui, 1991): 5 6

4

r = k column d

where

{ } is the member end force vector d = {d , d , d , d , d , d } is the member end displacement vector r = r1 , r2 , r3 , r4 , r5 , r6

T

T

1

Lc

2

3

4

5

6

EI = Constant

2

3

(2.48)

1

FIGURE 2.11 2-D column element.

50


and:

k column

 12  2 φ1  Lc      EI = c Lc       sym.   

6 φ Lc 2

0 A Ic

−

12 φ Lc2 1

0

0

4φ3

−

0 A Ic

−

6 φ Lc 2

0

12 φ Lc2 1

0 A Ic

     0   2φ4    6  − φ2  Lc   0   4φ3   6 φ Lc 2

(2.49)

is the column stiffness matrix, whereby For a tensile axial force:

( kL ) sinh kL 3

φ1 =

c

c

12(2 − 2 cosh kLc + kLc sinh kLc ) kL ( kL ) ( cosh 2

φ2 =

φ3 =

φ4 =

c

c

)

−1

6(2 − 2 cosh kLc + kLc sinh kLc )

)

kLc ( kLc cosh kLc − sinh kLc 4(2 − 2 cosh kLc + kLc sinh kLc )

)

kLc ( sinh kLc − kLc 2(2 − 2 cosh kLc + kLc sinh kLc )

(2.50a) (2.50b) (2.50c) (2.50d)

and for a compressive axial force:

( kL )

3

φ1 =

c

sin kLc

12(2 − 2 cos kLc − kLc sin kLc )

( kL ) ( 1 − cos kL )

(2.51a)

2

φ2 =

φ3 =

φ4 =

c

c

6(2 − 2 cos kLc − kLc sin kLc )

)

kLc ( sin kLc − kLc cos kLc 4(2 − 2 cos kLc − kLc sin kLc )

)

kLc ( kLc − sin kLc . 2(2 − 2 cos kLc − kLc sin kLc )

(2.51b) (2.51c) (2.51d)

In the above equations, k is defined in Equation 2.6. If the axial force in the column is zero, it can be shown by applying the L’Hospital rule successively that ϕ1 = ϕ2 = ϕ3 = ϕ4 = 1. For a small axial force, the above equations may become numerically unstable. To circumvent this situation and also to avoid the use of different expressions for


51

compressive and tensile forces, a power series expansion (Goto and Chen, 1986) can be used to simplify the expressions to:

24 n + 1 n   ( )  kL 2  n  1 ( kL )2   / 1 + φ1 = 1 + ∑ ( )   ∑ c       n =1 ( 2n + 4 )!  c    n =1 ( 2n + 1)!   

24 n + 1 n   ( )  kL 2  n  2 ( kL )2   / 1 + φ2 = 1 + ∑ ( )   ∑ c       n =1 ( 2n + 4 )!  c    n =1 ( 2n + 2 )!    6 n +1  ( )  kL 2  n  / 1 + 24 ( n + 1)  kL 2  n  φ3 = 1 + ∑ ( c )    ∑ ( c )    n =1 ( 2n + 3)!   n =1 ( 2n + 4 )! 

24 n + 1 n   ( )  kL 2  n  6 ( kL )2   / 1 + φ4 = 1 + ∑ ( )   ∑ c       n =1 ( 2n + 4 )!  c    n =1 ( 2n + 3)!   

(2.52a) (2.52b) (2.52c) (2.52d)

where the quantity:

( kLc )2 =

PLc2 EI c

(2.53)

is positive for a tensile force and negative for a compressive force. Because the stiffness matrix expressed in Equation 2.49 is a function of the axial force in the member, which depends on the displaced configuration of the structure that is not known in advance, the solution can only be obtained through an iterative process. The beam stiffness matrix kbeam and the column stiffness matrix kcolumn can be assembled to form the structure stiffness matrix K for a given structure. The critical load Pcr can be obtained from the characteristic equation:

det K = 0

(2.54)

Example: To demonstrate the above procedure for the bifurcation analysis of a semi-rigid frame, the pinned-based portal frame shown in Figure 2.12a is used. The frame is subjected to a pair of concentrated loads applied to the columns. The connections at both ends of the beams are assumed to be identical. When the loads attain their critical values, the frame will buckle. Since the frame is unbraced, the preferred buckling mode will be the sway mode as shown in Figure 2.12b. The sway-buckling mode of the frame can be uniquely defined by three displacement variables θA, θB, and Δ as shown in the figure. By assembling the column and beam element stiffness matrices, the stiffness relationship of the frame can be expressed as:

 2φ4  4φ3   0    = EI  4φ3 + sii* + sij*  0  L   0    sym. 

6 φ L 2 6 − φ2 L 12 φ L2 1 −

    θA    θB   ∆  

    

(2.55)

52


P

P

Pcr B

L

Pcr

θB

θA

EI = Constant

A

L a

L b

FIGURE 2.12 Buckling analysis of a semi-rigid portal frame.

or symbolically:

R = 0 = KD

(2.56)

det K. = 0

(2.57)

For a nontrivial solution, we must have:

The critical loads computed using various Rki = Rki L EI values where Rki is the initial stiffness of the connections are given in Table 2.2. Also shown in the table are the critical load ratios of the semi-rigid frames when compared to a rigid frame of the same dimensions. As can be seen, the change in Pcr is rather drastic when Rki is small, but it becomes less noticeable as Rki increases. When Rki = 20, the buckling load of the semi-rigid frame reaches 92.3 percent that of the corresponding rigid frame.

2.4.1.2 Load Deflection Analysis of Semi-rigid Frames

In a bifurcation analysis only the magnitude of the critical or bifurcation load is obtained. No information regarding the magnitude of deformation at bifurcation or the behavior of the frame after bifurcation of equilibrium can be obtained. To obtain such information, a load-deflection analysis is required. Figures 2.13a and 2.13b show the post-bifurcation load-lateral deflection behavior of a rectangular semi-rigid portal frame with and without imperfections (Goto et al., 1991). The frame in Figure 2.13a is subjected to a uniformly distributed load applied on the beam, whereas the frame in Figure 2.13b is subjected to a pair of concentrated loads applied on the columns. The magnitude of the concentrated loads is such that they give the same value of vertical load on the frame as does the distributed load. From the figures it can be seen that the behavior of the frame differs quite substantially depending on the type of vertical loads applied. In the figures, the solid line represents the behavior of the perfect frame and the dashed line represents the


53

TABLE 2.2 Buckling load comparison for a semi-rigid portal frame Rki

Pcr L2/EI

Pcr, semi-rigid /Pcr, rigid

0.5

0.398

0.219

1

0.659

0.362

2

0.976

0.536

4

1.28

0.703

6

1.42

0.78

8

1.51

0.83

10

1.56

0.857

12

1.6

0.879

14

1.63

0.896

16

1.65

0.907

18

1.67

0.918

20

1.68

0.923

∞ (rigid)

1.82

1

behavior of the imperfect frame. Imperfections are induced by applying a small lateral load equal to αPcr to the frame. For the perfect frame subjected to a uniformly distributed load, the postbifurcation load-deflection curve rises above the bifurcation load and does not experience stability failure until the limit point is reached. On the contrary, for the perfect frame subjected to the concentrated loads, the post-bifurcation load-deflection curve drops drastically after bifurcation indicating that no post-buckling strength is present. The reason for this behavior can be explained in terms of the loading and unloading behavior of the connections. For the frame subjected to the distributed load, the connections start to load as soon as the load is applied. As the applied load increases, the stiffness of the connections decreases because

ΣP / Pcr

ΣP = 2P

ΣP = wL w

αPcr

ΣP / Pcr h = 7.31 m

L = 7.31 m

1.0

h = 7.31 m L = 7.31 m

α=0

α=0 0.5

α = 3x10-3

× Critical load, Pcr

× Critical load, Pcr

Limit load

a

0

0.05

0.10

P

αPcr

1.0

α = 5x10-3

0.5

P

Limit load

0.15

∆/h

b

0

0.05

0.10

0.15

FIGURE 2.13 Behavior of a simple portal frame under different load types: (a) portal frame under a distribution load; (b) portal frame under concentrated loads.

∆/h

54


the slope of the connection moment-rotation curve decreases at higher values of moment (Figure 2.1). At bifurcation, the connections undergo unloading as a result of joint rotation when the columns buckle. When a connection unloads, its stiffness increases because the unloading stiffness is larger than its instantaneous stiffness prior to unloading (Figure 2.2). This increase in connection stiffness enhances the frame stiffness. Hence, additional loads can be applied beyond bifurcation. On the other hand, if concentrated loads are applied on the columns, none of the connections undergo loading until bifurcation. Once bifurcation occurs, the connections begin to load and so their instantaneous stiffness and hence the stiffness of the frame will continue to degrade. Thus, no additional loads can be applied beyond bifurcation. For the imperfect frame, except for the disappearance of the bifurcation point, the behavior when subjected to the two types of vertical loads is similar to its perfect counterpart. Note that when subjected to the uniformly distributed load, the limit load of the imperfect frame rises above the bifurcation point of its perfect counterpart, indicating that the bifurcation load of the perfect system is a conservative estimate of the stability limit state of the imperfect system. On the contrary, if the imperfect frame is subjected to the concentrated loads, the limit load always falls below the bifurcation point of its perfect counterpart, indicating that the bifurcation load is an unconservative estimate of the stability limit state of the frame. This observation is valid even for semi-rigid frames that are subject to a history of cyclic wind load before and after the application of the gravity load.

2.4.1.3 Allowance for the Formation of Plastic or Connection Hinges

When the bending moment at a particular location in the semi-rigid frame equals the plastic moment capacity of the cross-section, a plastic hinge will develop. Similarly, when the moment in the connection equals Mcn, a connection hinge is said to have formed. If strain hardening is neglected and if Mcn is taken as the maximum moment a connection can withstand, no additional moment beyond the hinge moment can be carried by the cross-section or the connection. Analysis of semi-rigid frames, taking into account the effect of concentrated plasticity in regions of plastic or connection hinges, can be carried out by casting kbeam and kcolumn of Equation 2.45 and Equation 2.48 in incremental form, and set the incremental moments at the hinge locations equal zero for any additional loading beyond Mp (for plastic hinge) or Mcn (for connection hinge) in subsequent cycles of analysis. Example: As an illustrative example, consider Figure 2.14 in which the load-deflection behavior of a fourstory frame is shown. The beams are W16 × 40 sections, the columns for the bottom story are W12 × 79 and other stories are W10 × 60 sections. All sections have a yield stress of 34.2 ksi (246 MPa). Two analyses were performed: One assumed the connections were rigid (dashed line), and the other assumed the connections were semi-rigid (solid line) with a moment-rotation behavior depicted in Figure 2.15. The numbers on the curves and next to the × sign on the frames indicate the sequence of plastic hinge formation as the magnitude of the applied loads increases monotonically. Note that the location of hinge formation differs starting from the sixth hinge. This is because the connection flexibility influences the distribution of moments in the frame. Another interesting observation is that although the sequence of hinge formation differs, the maximum loads the two frames can carry do not differ significantly. It has been shown (Poggi and Zandonini, 1985; Chen and Zhou, 1987) that if the connections possess moment capacities in excess of their adjoining members (i.e., full strength connections), the ultimate load capacity of the semi-rigid frame will not differ significantly from that of a rigidly-jointed frame.


67 4 5 67 8 9 5 4 3

1.00 3 2 1

Load, P/Pc

0.75

1

55

P/2

8 9 10

αP/2 αP αP

2

αP Rigid connection

0.5

0

1.0

1.5

2.0

10 ∆

7

3

4

2

5

1

H = 48 ft 8 6

7

9

0

9

all stories)

Rigid connection

α = 0.2403 Pc = 20.1 tons

0.25

P/2 (Typical of

30 ft

Flexible connection

0.50

P

2.5

Drift, ∆/H

6

3

4

2

5

1 8

(%)

Flexible connection

FIGURE 2.14 Comparative analysis of a four-story frame.

3000

Moment (kip-in)

2500 2000 1500 1000 500 0

0

10

20

30

40

50

60 70 -3 Rotation (x10 radians)

FIGURE 2.15 Connection moment rotation behavior (1 kip-in = 0.113 kN-m).

80

90

100

56


2.4.2 Design of Semi-rigid Frames

Over the years, a number of design approaches for semi-rigid frames have been proposed ( Lui, 1988; King and Chen, 1993; Xu and Grierson, 1993; Xu et al., 1995; Cabrero and Bayo, 2005). Some of these design methods have been summarized by Chen and Lui (1991), Chen et al., (1996), Chen (2000), and Faella et al. (2000). Generally speaking, the design of semi-rigid frames is complicated by the fact that almost all connections exhibit some type of nonlinear M-θr behavior and allowance for this nonlinear behavior in the design will lead to a nonlinear problem. However, the design of semiframes can be greatly facilitated by the use of some simplifying assumptions. In this section, a simple semi-rigid frame design approach will be discussed.

2.4.2.1 Design of Sway-prevented Semi-rigid Frames

Sway-prevented or nonsway frames are defined here as frames for which sufficient bracings are provided to limit the lateral deflection to a negligible value. In terms of design, a sway-prevented frame differs from a sway-permitted frame in that the loading and unloading behavior of the connections in a nonsway frame is not an important design consideration, and the K factor for columns in a nonsway frame can conveniently and conservatively be taken as unity. 2.4.2.1.1 Design of Beams Refer to Figure 2.16 in which the moment diagrams and maximum deflection values of a beam subjected to a uniformly distributed load of w under three different end support conditions (pinned, partially restrained, and fixed) are shown. From these diagrams, it can be seen that the design moment of the beam for the partially restrained case is always less than that of the pinned or fixed case. Since all types of connections offer a certain degree of partial restraint to the beam they connect, it is logical to design the beam as partially restrained members. The advantages involve not only a reduction in beam size but a reduction in beam deflection. Therefore, consideration of end restraint in design serves the dual purpose of reducing construction cost and improving the serviceability limit state of the structure.

w

Pinned supports

wLb2 8

+

Lb M

0 < Mneg < w

−

Partially restrained supports

wLb2 wLb2 < Mpos < 8 24

−

− +

Lb Fixed supports (a) Beams with different support conditions

wLb4 5wLb4 < δmax < 384EIb 384EIb

−

M

w

5wLb4 384EIb

wLb2 12

+

Lb

δmax =

wLb2 12 wLb2 24

M (b) Moment diagrams

δmax =

wLb4 384EIb

(c) Deflection formulas

FIGURE 2.16 Effect of end restraint on beam moments and deflections: (a) beams with different support conditions; (b) moment diagrams; (c) deflection formulas.


57

w δ θr

L

= w δss

θss

+ θM δM Mneg

Mneg

FIGURE 2.17 Load effects on a partially restrained beam.

If linearly elastic material behavior is assumed, the amount of decrease in design moment and deflection for the partially restrained beam shown in Figure 2.16 can be calculated readily using the principle of superposition. Consider Figure 2.17 in which the load effects on the partially restrained beam are decomposed into two load cases. The first load case corresponds to a simplysupported beam subjected to the uniformly distributed load. The second load case represents the restraining effect on the beam from the connections. Compatibility of rotation at the ends requires that:

θr = θ ss + θ M

(2.58)

where θr is the rotational deformation of the connection, θss is the end rotation of a simply-supported beam due to the uniformly distributed load and θM is the end rotation of the beam due to the restraining moment. Substituting:

M neg θr = Rk

(2.59)

where Mneg is the negative beam end moment, Rk is the connection stiffness, and:

wL 3 θ ss = b 24 EI b

(2.60)

− M neg Lb θM = 2 EI b

(2.61)

58


into Equation 4.58 and solving for Mneg, we obtain: M neg =

2 Rk M 3 ( Rk + 2 ss

(2.62)

)

In the above equation, Rk = Rk Lb EI b is the nondimensional connection stiffness, and Mss = wLb2/8 is the maximum moment of a uniformly loaded simply-supported beam. Once Mneg is calculated, the positive moment of the partially restrained beam can be evaluated from: M pos = M ss − M neg

(2.63)

Substituting Equation 2.62 for Mneg into Equation 2.63 gives:  R +6  M pos =  k  M ss  3 Rk + 6 

(2.64)

Equations 2.62 and 2.64 are plotted in Figure 2.18. As can be seen, both the negative and the positive moments of the partially restrained beam fall below the simple beam moment Mss. Mneg/ Mss will approach a value of 0.667, and Mpos/Mss will approach a value of 0.333. These values correspond to the case when the ends of the beam are fixed. From the standpoint of the beam, an optimal design can be achieved by enforcing the condition that Mneg = Mpos = 0.5Mss. This condition is depicted in Figure 2.18 as the intersection of the two curves. The nondimensional connection stiffness that corresponds to this condition is 6 for the uniformly loaded beam case. Also shown in Figure 2.18 is the range within which the semi-rigid nature of the connections should be taken into account. The range is 2 < Rk < 20. For Rk ≤ 2, the connection can practically be assumed as pinned, and for Rk ≤ 20, the connection can practically be assumed as rigid. Although Equation 2.62 provides a convenient means to estimate Mneg for design, another approach to estimate Mneg was proposed by Nethercot et al. (1988). By performing a series of beam M Mss 1.0

Semi-rigid range

0.8

Mneg Mss

0.6 0.4

Mpos Mss

0.2 0

0

2

4

6

8

10

12

14

16

18

20

22

Rk = RkLb /EIb FIGURE 2.18 Relationships between moments and connection stiffness.


59

analyses using commonly encountered beam span-to-depth ratios with partial restraint provided by three types of connection: double web angles; flush end plate; and extended end plate, Nethercot et al. (1988) recommended that the following values for Mneg be used for the design of laterally supported beams: 8% of Mpb 45% of Mpb 60% of Mpb

Double web angles: Flush end plate: Extended end plate:

where Mpb is the plastic moment capacity of the beam. In addition to reducing the design moment, the presence of connections also reduces the deflection of the beam. Referring once again to Figure 2.17 and using superposition, the midspan deflection of the partially restrained beam can be written as:

δ = δ ss + δ M

(2.65)

where δss = 5wLb4/384EIb is the midspan deflection of a uniformly loaded simply-supported beam and δM = −MnegLb2/8EIb is the midspan deflection due to Mneg. Substituting Equation 2.62 for Mneg into the expression for δM, Equation 2.65 can be written as:  R + 10  δ = k  δ ss  5 Rk + 10 

(2.66)

Equation 2.66 is plotted in Figure 2.19. Note that the decrease in deflection is rather rapid in the range 0 < Rk < 10. The curve levels off and becomes asymptotic to a value of 0.2 when the fixedend condition is approached. In designing the partially restrained beam shown in Figure 2.17, a proper value for Rk must be used. Generally, it is inadvisable to use the initial stiffness value Rki, since this represents an upper bound value for the connection stiffness. For design purposes, a secant stiffness obtained by intersecting the connection moment-rotation curve by a beam line under factored gravity load (i.e., the moment created by the factored gravity load as indicated by Mg in Figure 2.3) can be used as the representative connection stiffness. Alternatively, if sufficient information on the connection moment-rotation behavior and a second-order analysis program are available, the actual connection stiffness and the amount of rotational restraint provided by the connections to the beam can be used for the design (Lindsey et al., 1985; Lindsey, 1987). δ δss 1.0

Semi-rigid range

0.8 0.6 0.4 0.2 0

0

2

4

6

8

10

12

14

16

18

20

22

Rk = RkLb /EIb

FIGURE 2.19 Relationship between deflection and connection stiffness.

60


2.4.2.1.2 Design of Columns Once the beams have been designed, the columns of the nonsway frame can be proportioned using the interaction equations provided in the design specifications. The equations are given by AISC (2005) as follows: For Pu/ϕPn ≥ 0.2: P u + 8  M ux + M uy  ≤ 1.0 (2.67a) φc P n 9  φ b M nx φ b M ny  and for Pu/ϕPn < 0.2:

 M ux M uy  Pu + +  ≤ 1.0 2 φc Pn  φb M nx φb M ny 

(2.68b)

where the subscripts x and y refers to strong and weak axes of the member, respectively, and:

Mn = design flexural strength of the member (see Section 2.3.1.1) Mu = maximum moment in the member accounting for second-order effect Pn = design compressive strength of the member (see Section 2.2.2.5) Pu = maximum axial force in the member accounting for second-order effect ϕc = resistance factor for compression = 0.90 ϕb = resistance factor for flexure = 0.90

Herein, to compute Pn, a K factor of unity is recommended for the sway-prevented frame. The moments acting at the ends of the column can be obtained from the end restrained moments of the beam distributed according to the relative stiffness of the columns above and below the beam, i.e.:

on either side of the column) M c = DF × ∑ ( Beam end moments

(2.68)

where DF is a stiffness distribution factor given by:

DF =

( EI L )c ∑ ( EI L )c

(2.69)

The summation in the denominator is to be carried out for all columns that are present above and below the beam-column joint.

2.4.2.2 Design of Sway-permitted Semi-rigid Frames

In the design of sway-permitted semi-rigid frames, the loading and unloading characteristics of the connections must be considered. To illustrate how the connections affect semi-rigid frame behavior, the next two paragraphs describe the response of a subassemblage (Figure 2.20a) representing a portion of a semi-rigid frame under gravity load subjected to one cycle of wind load. Under the action of a factored gravity load, the moments at the ends of a typical girder can be obtained as the intersection of the connection moment-rotation curve and the beam line. This is shown as Point 1 in Figures 2.21a and 2.21b for connections A and B, respectively. When a wind or lateral force acts on the subassemblage (Figure 2.20b), connection A unloads while connection B loads. The states of moments for the two connections at the end of this stage are denoted by Point 2 in Figure 2.21. When the wind load is removed, the frame undergoes an elastic rebound (Figure 2.20c) and consequently, connection A will reload while connection B unloads. The states of moments for the connections that correspond to this stage are denoted by Point 3 in Figure 2.21. For connection A, Point 3 is below Point 1 because of the P-Δ effect. The vertical force acting through the lateral displacement caused by the wind load tends to prevent the frame from snap-


61

Wind A

B

A

(a)

B (b) Wind

A

B

A

(c)

B (d)

Wind A

B

A

(e)

B (f)

FIGURE 2.20 Semi-rigid frame subassemblage.

M

M

1

3

2

4

6

1

3

5

5

2 a

6

θr

b

4

θr

FIGURE 2.21 States of moments in connections A and B: (a) connection A; (b) connection B.

ping back to its original configuration. As a result, the equilibrium position of the frame is slightly swayed to the direction of the wind even after the wind load is removed. Because of this swaying, positive moment is induced in connection A, causing Point 3 to be below Point 1. If the wind blows from the other direction as shown in Figure 2.20d, connection A will load and connection B will unload. The states of moments at the end of this stage are denoted as Point 4 in Figure 2.21. Upon removal of this wind load (Figure 2.20e), connection A will unload to Point 5 in Figure 2.21a and connection B will reload to Point 5 in Figure 2.21b. Point 5 is below Point

62


3 for connection B because of the P-Δ effect as explained earlier. Finally, to complete the cycle, when the wind blows again in the original direction (Figure 2.20f), connection A will unload and connection B will reload to Point 6 as shown in Figures 2.21a and 2.21b, respectively. Note that if the cycle is repeated, both connections will behave elastically with the initial connection stiffness governing the behavior of both connections. Figure 2.22 shows the corresponding bending moment diagrams for the beam during the complete cycle of loading. Note that for all stages of loading, negative moment(s) is (are) likely to be present at the beam end(s). Therefore, to design the beam as if its ends were hinged is a rather conservative approach. It should be mentioned that Point 6 of Figure 2.21a for connection A and Point 4 of Figure 2.21b for connection B are usually small in real frames. Therefore, it is justified to reduce the positive moment in the design of the beam. To simplify the design process, only two parameters Rki and Mcn will be used. To begin the design, the connections are first proportioned to carry the shear from factored gravity loads on the beam. These connections must be designed to sustain large inelastic rotation without failure as stipulated in the AISC Specifications. Rki and Mcn are then determined. As indicated earlier, Rki can be conservatively taken as the secant stiffness of the connection under factored gravity load. As for Mcn, its value can be determined graphically as shown in Figure 2.23. Having determined these two parameters, the design of the beam can now proceed. 2.4.2.2.1 Design of Beams If Mcn of the connection is smaller than Mpb of the adjoining beam, Mneg in Figure 2.22 can be approximated by Mcn. Otherwise, Mneg needs to be determined from structural analysis. In addition

A

−

+

−

B

−

A −

+

(b)

(a)

A

−

+

−

B

A

−

−

+

B

+

(d)

(c)

A

B

−

(e) FIGURE 2.22 Bending moment diagrams.

B

A

− +

(f)

B


63

M Mcn Mg

Rki 1

θr

a

M Mcn Mg

Rki 1 b

θr

FIGURE 2.23 Determination of Rki and Mu for design: (a) connection without strainhardening stiffness; (b) connection with strain-hardening stiffness.

to knowing Mneg at one end, we need to know the moment at the other end of the beam to proceed with the beam design, so the amount of reduction in positive moment can be determined. From Figure 2.22, it can be seen that the most severe loading cases are those of Figure 2.2d and 2.2f. For design purposes, the positive end moment can be taken as zero. To approximate the positive end moment by zero does not seem conservative at first glance. However, it should be noted that this positive end moment (which corresponds to Point 6 or Point 4 in Figures. 2.21a and 2.21b, respectively) is in reality small and, additionally, it occurs as a result of frame sway. The amount of sway of a semi-rigid frame is controlled by the drift limit. In actual frameworks, the satisfaction of the drift requirement will limit this positive moment to a small value. With the two beam end moments known, the maximum positive moment of the beam can be obtained easily using elementary structural analysis. The beam can then be proportioned according to this moment or Mneg, whichever is larger.

64


P2

P1 Unloads

Mu Wind

P3

P1

Unloads MuL

P2 DF x Mu

DF x (MuR − MuL )

DF x Mu

DF x (MuR − MuL )

Loads

MuR

Loads

Unloads Mu Unloads

Loads

MuR

MuL Loads

P1

P2

P3

(a)

P1

P2

Windward exterior column

Interior column

(b)

(c)

FIGURE 2.24 Determination of column end moments.

2.4.2.2.2 Design of Columns For a sway-permitted exterior windward column, both the top and bottom connections undergo unloading when the frame sways and thus rotational restraints are offered to both ends of the column by the beams (Figure 2.24a). The free-body diagram for the design of this beam-column is shown in Figure 2.24b. In the diagram, DF is the stiffness distribution factor given in Equation 2.69, Mu is the moment from the beam, which can be taken as Mcn (if Mcn ≤ Mp) or determined from structural analysis (if Mcn > Mp). The exterior leeward column, however, does not have any rotational restraint from the beams since both connections undergo loading as the frame sways (Figure 2.24a). As a result, the exterior leeward column cannot participate in frame stability and the stability of the frame needs to be provided by the remaining exterior windward and interior columns. The behavior of the sway-permitted interior column is similar to that of the exterior windward column in that rotational restraints at both ends of the column are provided by the beams that frame into the leeward side of the column (Figure 2.24a). The free body diagram of the beamcolumn to be designed is shown in Figure 2.24c.

2.4.3 Drift of Semi-rigid Frames

Following the design of the beams and columns, the frame must be analyzed for drift to ensure that excessive lateral deflection does not occur. As a result of the connection flexibility, semi-rigid frames tend to deflect quite significantly under the action of lateral loads (Gerstle and Ackroyd, 1990). Studies have shown that most flexibly-connected frames designed on the basis of strength violate the drift requirement for serviceability. If the amount of drift exceeds the intended tolerance limit, the lateral stiffness of the frame must be increased. The lateral stiffness of semi-rigid frames can be enhanced by instituting one or a combination of the following measures: (1) provide bracings; (2) increase the member size; and/or (3) use stiffer connections.


65

Although a spreadsheet application for approximate drift calculations was proposed by Ackroyd (1990) for semi-rigid frames, the following prediction formulas (Cronembold and Ackroyd, 1986; Gerstle and Ackroyd, 1990) for drift can be used for a preliminary analysis. For top and seat angles: ∆ W = H 90 + 160 ( B H

(2.70)

)

For flange plates ∆ W = H 130 + 160 ( B H

(2.71)

)

In the above formulas, Δ is the lateral deflection at the top story of the semi-rigid frame, H is the overall height of the frame, B is the overall width of the frame, and W is the lateral load intensity (in kips/ft of vertical height). If an idealized connection model is used in which the unloading connection stiffness is taken as Rki and the loading connection stiffness is taken as 0, frame drift can be obtained by analyzing the frame as a rigidly connected frame provided that I of all the beams with semi-rigid connections are replaced by I computed using Equation 2.14. Example: The semi-rigid fixed based portal frame shown in Figure 2.25 is to be designed. The frame is braced against out-of-plane deformation at all beam-column joints. This means the lateral unbraced length of the beam is 20 ft. (6.1 m), and the effective length factor for weak axis (i.e., out-of-plane) bending of the columns can conveniently be taken as 1. The effective length factor for strong axis (i.e., in-plane) bending still needs to be computed using the procedure outlined in Section 2.2.2.3. The connections are assumed to possess a stiffness of Rki =15 and Mcn = 250 k-ft (339 kN-m). The loads to be designed for are: uniformly distributed dead load, D = 2 k/ft (29.2 kN/m); uniformly distributed live load, L = 3 k/ft (43.8 kN/m); and wind load, W= 2.5 kips (11.1 kN). The lateral deflection of the frame is to be limited to H/300. Use A992 steel (Fy = 50 ksi or 345 MPa) and wide flange (W) shapes for all members. From AISC (2005), the load combinations that most likely will control the design are: 1.2D + 1.6L 1.2D + 1.6W + 0.5L

B

C

Rk =15 A

12 ft. (3.7 m) D

20 ft. (6.1 m) FIGURE 2.25 Design of a semi-rigid portal frame.

66


Thus, a factored uniform load of wu=7.2 k/ft (105 kN/m) for the first load case, and a factored uniform load of wu=3.9 k/ft (56.9 kN/m) and a factored wind load of Wu=4 kips (17.8 kN) for the second load case will be used for the design. Under the first (gravity only) load case, the frame will not undergo any sidesway, as a result Equation 2.62 and Equation 2.64 can be used to estimate Mneg and Mpos, respectively. Substituting Rki = 15 into these equations gives Mneg = 212 k-ft (287 kN-m) and Mpos = 182 k-ft (247 kN-m), thus Mneg controls. Since this value is less than Mcn, the beam will be selected based on Mneg, i.e., Mu is to be taken as Mneg. It is important to note that these moment values are only approximate because the bending stiffness of the columns has not been taken into consideration. If the effect of column flexibility is taken into consideration, the actual end restraint provided to the beam will be less than Rki =15. From simple equilibrium consideration and neglecting the self-weight of the members for the time being, Pu in the column can be determined to be 72 kips (320 kN). The objective here is to select a beam section so that its design strength ϕbMn (where ϕb = 0.9 and Mn is to be determined using the equations in Section 2.3.1.1) exceeds the required strength Mu, and to select a column section that satisfies the appropriate interaction equation in Section 2.4.2.1.2. Using the equations from Section 2.3.1.1, a W12 × 53 section is selected for the beam; and using Equation 2.67b, a W10 × 60 section is selected for the columns. Now, with the preliminary beam and column sections selected, a second order analysis taking into consideration the applied loads and the member weight is carried out for both load cases. The results for the required strengths are given in the following tables: Load case 1 (1.2D + 1.6L) − Gravity only Member

Pu kips (kN)

Mu k-ft (kN-m)

Beam

20 (89)

204 (277)

Left column

73.25 (326)

160 (217)

Right column

73.25 (326)

160 (217)

Load Case 2 (1.2D + 1.6W + 0.5L) − Gravity plus wind Member

Pu kips (kN)

Mu k-ft (kN-m)

Beam

6 (26.7)

166 (225)

Left column

43.5 (194)

64.2 (87.1)

Right column

37.0 (165)

73.7 (100)

As can be seen, the gravity-only load case controls the design. It should be noted that in carrying out the analysis for load case 2, the connection at the leeward side of the frame, which is undergoing loading, is conservatively assumed to have zero stiffness. Also, because the required axial strength for the beam is relatively small, the beam can be designed as a flexural member, whereas the columns must be designed as beam-columns. To complete the design the sections are to be checked for both load cases: For the W12 × 53 section, the design flexural strength ϕbMn computed using Equation 2.23 with ϕb = 0.9 and Cb = 1 is 231 k-ft (313 kN/m). This exceeds the required flexural strength Mu = 204 k-ft (277 kN-m) for the first load case, and Mu = 166 k-ft (225 kN-m) for the second load case. Therefore, the section is adequate.


67

For the W10 × 60 section, the design axial strength ϕcPn computed using Equation 2.19a with ϕc = 0.9, (KL)y = 12 ft. (3.66 m) for the gravity-only load case, and (KL)x = 25.2 ft. (7.7 m) for the gravity-plus-wind load case, for the right column are 631 kips (2810 kN) and 560 kips (2500 kN), respectively. The design flexural strength ϕbMn computed using Equation 2.23 with ϕb = 0.9, Lb = 12 ft (3.7 m) and Cb = 1 is 269 k-ft (365 kN-m). Substituting these values with Pu = 73.25 kips (326 kN) and Mu = 160 k-ft (217 kN-m) for the first load case, and Pu = 37.0 kips (165 kN) and Mu = 73.7 k-ft (100 kN-m) for the second load case into Equation 2.67b gives 0.65 and 0.31 for the two load cases, respectively. Thus, the interaction equation is satisfied, and so the section is adequate. Finally, under a service wind load of 2.5 kips (11.1 kN), the lateral deflection experienced by the semi-rigid frame is 0.4 in. (10 mm). This is less than the specified allowable lateral deflection value of H/300=0.48 in. (12.2 mm). Therefore, the serviceability limit state is also satisfied.

2.5 Summary and Conclusions The analysis and design of semi-rigid frames are intrinsically more complex than their rigid counterparts because of the difficulty and uncertainty in predicting the moment-rotation behavior of the connections. Fortunately, studies by Goto and Chen (1987), Wu and Chen (1990), and others have demonstrated that minor errors in predicting the response of the connections will not noticeably affect the overall behavior of the semi-rigid frame. Experiments carried out on steel beam-to-column connections over the past decades have demonstrated clearly that the response of a connection is nonlinear when the connection is undergoing loading but becomes more or less linear when it is undergoing unloading. Various mathematical models to represent the connection M-θr behavior have been proposed. Some of these models have been summarized in Section III of this handbook. There is no ironclad rule as to which model is the best. Each has its advantages and disadvantages. Nonetheless, all of these models can represent the M-θr behavior of the connection fairly well and they have all been successfully used in the analysis of semi-rigid framed structures. Based on a number of studies on semi-rigid frame behavior under combined gravity and lateral loads, the following conclusions can be made:

1. If the nominal moment capacity of a connection is larger than the maximum moment it experiences during the entire load history of the frame, the maximum load-carrying capacity of the frame is independent of the types of connection used. 2. Although the maximum load-carrying capacity of the frame may not be affected by the connection, the frame with flexible connections does deform more. 3. Inelasticity in the column may cause the column to shed its moment to the beam provided that the beam remains elastic. The more flexible the connection is, the later the column will shed its moment to the beam because less moment is transmitted to the column from the beam. 4. Connection flexibility may cause early nonlinear behavior for the frame and the loading and unloading characteristics of the connection will alter the moment distribution in the frame. 5. The use of bracing can drastically reduce the drift of the frame and the presence of bracing seems to obscure the nonlinear behavior of the connections (Lui and Chen, 1988). Because of this, a linear elastic frame analysis may be sufficient for flexibly connected frames loaded in the service load range.

The simplest approach to design semi-rigid frames is to assume that the connections provide no restraint to the beams. The beams are therefore designed as simply-supported members insofar

68


as gravity loads are concerned. On the other hand, the columns are designed assuming that the connections can provide full rotational restraint for lateral loads. This approach, proposed by Disque (1975), while historically safe, often results in a design in which the beams are oversized and the columns are undersized. A more rational approach, in light of the limit state philosophy should therefore be used. If a second-order analysis program is available which can take into consideration connection flexibility, it should be used for design. In lieu of such a program, simplified design methods which are based on simplified behavioral models for connections and for semi-rigid frame action can be used. One such simplified method has been discussed in this chapter. The method requires the use of only two connection parameters Rki (taken as the secant stiffness of the connection under factored gravity load) and Mcn (obtained graphically from the connection M-θr curve), and is considered a compromise between accuracy and simplicity. It is important to note that the method proposed is strength based, which means that the design is based on strength, not serviceability. Since excessive frame drift is often a problem for semi-rigid frames, due consideration must be given to check the resulting design for serviceability requirements and proper measures must be taken to limit the drift of semi-rigid frames.

References Ackroyd, M. H., Electronic spreadsheet tools for semi-rigid frames, AISC Engineering Journal, 27(2), 69–78, 1990. AISC, Steel Construction Manual, 13th edition, American Institute of Steel Construction, Chicago, IL. Aristizabal-Ochoa, J. D., Stability and second-order analysis of frames with semi-rigid connections under distributed loads, Journal of Structural Engineering, ASCE, 127(11) 1306–1315, 2001. Aristizabal-Ochoa, J. D., Story stability of braced, partially-braced, and unbraced frames: Classical approach, Journal of Structural Engineering, ASCE, 123(6), 799–806, 1997. Aristizabal-Ochoa, J. D., K-factor for columns in any type of construction: Nonparadoxical approach, Journal of Structural Engineering, ASCE, 120(4), 1272–1290, 1994. ASCE, Effective Length and Notional Load Approaches for Assessing Frame Stability: Implications for American Steel Design, Task Committee on Effective Length, ASCE, 1997. Cabrero, J. M. and Bayo, E., Development of practical design methods for steel structures with semi-rigid connections, Engineering Structures, 27(8), 1125–1137, 2005. Cerfontaine, F. and Jaspart, J. P., Analytical study of the interaction between bending and axial force in bolted jointed, In: Eurosteel, Coimbra, 997–1006, 2002. Chapius, J. and Galambos, T. V., Restrained crooked aluminum columns, Journal of the Structural Division, ASCE, 108(ST3), 511–524, 1982. Chen, W. F. (editor), Practical analysis for semi-rigid frame design, World Scientific, Singapore, 2000. Chen, W. F., Goto, Y., Liew, J. Y. R., Stability design of semi-rigid frames, John Wiley and Sons, New York, NY, 1996. Chen, W. F. and Lui, E. M., Stability design of steel frames, CRC Press, 1991. Chen, W. F. and Lui, E. M., Structural stability—Theory and implementation, Elsevier, 1987. Chen, W. F. and Lui, E. M., Effects of joint flexibility on the behavior of steel frames, Computers and Structures, 26(5), 719–732, 1987. Chen, W. F. and Zhou, S. P., Inelastic analysis of steel braced frames with flexible joints, International Journal of Solids and Structures, 23(5), 631–649, 1987. Chikho, A. H. and Kirby, P. A., An approximate method for estimation of bending moments in continuous and semi-rigid frames, Canadian Journal of Civil Engineering, 22, 1120–1132, 1995. Cronembold, J. R. and Ackroyd, M. H., Economy and safety of semi-rigid frame design: Case studies, Stability of Tall Steel Buildings, Workshop Proceedings, Third International Conference on Tall Buildings, Bethlehem, PA, Council on Tall Buildings and Urban Habitat, Chicago, IL, 113–171, 1986.


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Cunningham, R., Some aspects of semi-rigid connections in structural steelwork, The Structural Engineer, 68(5), 85–92, 1990. Disque, R. O., Directional moment connections—A proposed design method for unbraced steel frames, AISC Engineering Journal, 12(1), 14–18, 1975. Faella, C., Piluso, V., and Rizzano, G., Structural steel semi-rigid connections—Theory, design and software, CRC Press, Boca Raton, FL, 2000. Frye, M. J. and Morris, G. A., Analysis of flexibly connected steel frames, Canadian Journal of Civil Engineers, 2(3), 280–291, 1976. Fukumoto, Y. and Itoh, Y., Statistical study of experiments on welded beams, Journal of the Structural Division, ASCE, 107(ST1), 89–103, 1981. Fukumoto, Y., Itoh, Y., and Kubo, M., Strength variation of laterally unsupported beams, Journal of the Structural Division, ASCE, 106(ST1), 165–181, 1980. Galambos, T. V., Inelastic lateral buckling of beams, Journal of the Structural Division, ASCE, 89(ST5), 217– 242, 1963. Gerstle, K. H. and Ackroyd, M. H., Behavior and design of flexibly-connected building frames, AISC Engineering Journal, 27(1), 22–30, 1990. Geschwindner, L. F., A simplified look at partially restrained beams, AISC Engineering Journal, 28(2), 73–78, 1991. Gizejowski, M. A., Branicki, C. J., Barszcz, A. M., and Krol, P., Advanced analysis of steel frames with effects of joint deformability and partial strength accounted for, Journal of Civil Engineering and Management, X(3), 199–208, 2004. Goto, Y., Suzuki, S., and Chen, W. F., Analysis of critical behavior of semi-rigid frames with or without load history in connections, International Journal of Solids and Structures, 27(4), 467–483, 1991. Goto, Y. and Chen, W. F., On the computer-based design analysis for flexibly-connected building frames, Journal of Constructional Steel Research, Special Issue on Joint Flexibility in Steel Frames, 8, 203–231, 1987. Julian, O. G. and Lawrence, L. S., Notes on J and L nomographs for determination of effective lengths, Jackson and Moreland Engineers, USA, 1959 (unpublished report). King, W. S. and Chen, W. F., LRFD Analysis for semi-rigid frame design, AISC Engineering Journal, 30(4), 130–140, 1993. Kishi, N., Hasan, R., Chen, W. F., and Goto, Y., Power model for semi-rigid connections, Steel Structures, Journal of Singapore Structural Steel Society, 5(1), 37–48, 1994. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K. G., Analysis program for the design of flexibly jointed frames, Computers and Structures, 49(4), 705–714, 1993a. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K. G., Design aid of semi-rigid connections for frame analysis, AISC Engineering Journal, 30(3), 90–107, 1993b. Kishi, N. and Chen, W. F., Moment-rotation relations of semi-rigid connections with angles, Journal of Structural Engineering, ASCE, 116(7), 1813–1834, 1990. Johnston, B. G. (editor), SSRC guide to stability design criteria for metal structures, 3rd edition, John Wiley, New York, NY, 1976. LeMessurier, W. J., A practical method of second order analysis, Part 2—Rigid frames, AISC Engineering Journal, 14(2), 49–67, 1972. Leon, R. T., Composite semi-rigid construction, AISC Engineering Journal, 31(2), 57–67, 1994. Lindsey, S. D., Design of frames with PR connections, Journal of Constructional Steel Research, 8, 251–260, 1987. Lindsey, S. D., Loannides, S., and Goverdhan, A. V., LRFD analysis and design of beams with partially restrained connections, AISC Engineering Journal, 22(4), 157–162, 1985. Lui, E. M., Stability design of partially restrained frames, Fifth International Colloquium on Stability of Metal Structures, Chicago, IL, 259–268, 1996. Lui, E. M., Column effective length factor for semi-rigid frames, Steel Structures, Journal of Singapore Structural Steel Society, 6(1), 3–20, 1995. Lui, E. M., A novel approach for K factor determination, AISC Engineering Journal, 29(4), 150–159, 1992.

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Lui, E. M. and Chen, W. F., Behavior of braced and unbraced semi-rigid frames, International Journal of Solids and Structures, 24(9), 893–913, 1988. Lui, E. M., A practical P-Delta analysis method for Type FR and PR frames, AISC Engineering Journal, 25(3) 85–98, 1988. Lui, E. M. and Chen, W. F., Steel frame analysis with flexible joints, Journal of Constructional Steel Research, 8, 161–202, 1987. Lui, E. M. and Chen, W. F., End restraint and column design using LRFD, AISC Engineering Journal, 20(1), 29–39, 1983. Monforton, A. R. and Wu, T. S., Matrix analysis of semi-rigid connected frames, Journal of the Structural Division, 87(6), 13–42, 1963. Nethercot, D. A., Davison, J. B., and Kirby, P. A., Connection flexibility and beam design in non-sway frames, AISC Engineering Journal, 25(3), 99–108, 1988. Poggi, C. and Zandonini, R., Behavior of strength of steel frames with semi-rigid connections, Proceedings in Connection Flexibility and Steel Frames, ASCE Convention, Detroit, MI, October, ASCE, NY, 57–76, 1985. Rodrigues, F. C., Saldanha, A. C., and Pfeil, M. S., Non-linear analysis of steel plane frames with semi-rigid connections, Journal of Constructional Steel Research, 46(1-3), 94–97, 1998. Sekulovic, M. and Nefovska-Danilovic, M., Static inelastic analysis of steel frames with flexible connections, Theoretical and Applied Mechanics, 31(2), 101–134, 2004. Timoshenko, S. P. and Gere, J. M., Theory of elastic stability, 2nd edition, McGraw-Hill, New York, 1961. Trahair, N. S., Flexural-torsional buckling of structures, CRC Press, Boca Raton, FL, 1993. Urbonas, K. and Daniunas, A., Behaviour of semi-rigid steel beam-to-beam joints under bending and axial forces, Journal of Constructional Steel Research, 62, 1244–1249, 2006. Urbonas, K. and Daniunas, A., Component method extension to steel beam-to-beam and beam-to-column knee joints under bending and axial forces, Journal of Civil Engineering and Management, XI(3), 217– 224, 2005. van Keulen, D. C., Nethercot, D. A., Snijder, H. H., and Bakker, M. C. M., Frames analysis incorporating semi-rigid joint action: Applicability of the half initial secant stiffness approach, Journal of Constructional Steel Research, 59, 1083–1100, 2003. Vinnakota, S., Inelastic stability of laterally unsupported I-beams, Computers and Structures, 7(3), 377–389, 1977. Wu, F. H. and Chen, W. F., A design model for semi-rigid connections, Engineering Structures, 12(2), 88–97, 1990. Xu, L. and Liu, Y., Story-based effective length factors for unbraced PR frames, AISC Engineering Journal, 39(1), 13–29, 2002. Xu, L., Grierson, D. E., and Sherbourne, A. N., Optimal cost design of semi-rigid, low rise industrial frames, AISC Engineering Journal, 32(3), 87–97, 1995. Xu, L. and Grierson, D. E., Computer-automated design of semi-rigid steel frameworks, Journal of Structural Engineering, ASCE, 119(6), 1740–1760, 1993. Yau, C. Y. and Chan, S. L., Inelastic and stability analysis of flexibly connected steel frames by spring-in-series model, Journal of Structural Engineering, ASCE, 120(10), 2803–2820, 1994. Yoshida, H. and Imoto, Y., Inelastic lateral buckling of restrained beams, Journal of the Engineering Mechanics Division, ASCE, 99(EM2), 343–366, 1973. Yura, J. A., Galambos, T. V., and Ravindra, M. K., The bending resistance of steel beams, Journal of the Structural Division, ASCE, 104(ST9), 1355–1369, 1978.

3

Types of PR Connections

Norimitsu Kishi Professor, Civil Engineering Unit, College of Environmental Engineering, Muroran Institute of Technology, Muroran 050-8585, Japan Masato Komuro Associate Professor, Civil Engineering Unit, College of Environmental Engineering, Muroran Institute of Technology, Muroran 050-8585, Japan

3.1 Single Web-angle Connections/Single Plate Connections................................................ 71 3.2 Double Web-angle Connections........................................................................................... 71 3.3 Top- and Seat-angle with Double Web-angle Connections.............................................. 73 3.4 Top- and Seat-angle Connections......................................................................................... 73 3.5 Extended End-plate Connections/Flush End-plate Connections..................................... 75 3.6 Header Plate Connections...................................................................................................... 75

References................................................................................................................................. 77

3.1 Single Web-angle Connections/Single Plate Connections Single web-angle connections consist of an angle either bolted or welded to both the column and the beam web, as shown in Figure 3.1. On the other hand, single plate connections use the plate instead of the angle (Figure 3.2). This connection type requires less material than does a single web-angle connection. Generally, in designing these connections, the single web-angle connections have moment rigidity equal to about one-half of the double web-angle connections, and the single plate connections have rigidity equal to or greater than the single web-angle connections, since one side of the plate is fully welded with the column flange.

3.2 Double Web-angle Connections Double web-angle connections consist of two angles, either bolted or riveted to both the column and the beam web, as shown in Figure 3.3. Rivets were used as fasteners in the earliest tests on double web-angle connections conducted by Rathbun (1936). In the 1950s, most specifications for the design of steel structures allowed the use of high-strength bolts instead of rivets. To clarify the effect of high-strength bolts on connection behavior when used in conjunction with rivets, Bell et al. (1958) and Lewitt et al. (1966) conducted experiments on riveted and bolted beamto-column connections. Today, high-strength bolts are used popularly as fasteners for this type 71

72


column

column angle

beam

FIGURE 3.1 Single web-angle connection.

column

plate beam

Welded

FIGURE 3.2 Single plate connection.


73

column web angle

beam

FIGURE 3.3 Double web-angle connection.

of connection. Though the connection rigidity of this type of connection is stiffer than those of single web-angle and single plate connections, the AISC-ASD specifications (1989) consider this connection type as a Type 2 construction (simple connection or shear connection).

3.3 Top- and Seat-angle with Double Web-angle Connections This type of connection is a combination of top- and seat-angle connections and double webangle connections. A typical top- and seat-angle connection with a double web-angle is shown in Figure 3.4. Double web angles are used to improve the connection restraint characteristics of top- and seat-angle connections, and for shear transfer. This type of connection is considered as Type 3 framing in the AISC-ASD specifications (1989) (i.e., a semi-rigid connection).

3.4 Top- and Seat-angle Connections A typical top- and seat-angle connection is shown in Figure 3.5. The AISC-ASD specifications (1989) described this type of connection as follows: (1) the top angle is used to provide lateral support of the compression flange of a beam; and (2) the seat angle is to transfer only the vertical reaction of the beam to the column and should not apply a significant restraining moment to the end of the beam. However, according to the experimental results, these connections will be able to transfer not only the vertical reaction, but also some end moment of the beam to the column.

74


column top angle

beam web angle

seat angle

FIGURE 3.4 Top- and seat-angle connection with double web-angle.

column top angle

beam

seat angle

FIGURE 3.5 Top- and seat-angle connection.


75

3.5 Extended End-plate Connections/Flush End-plate Connections In general, end-plate connections are always welded to the web and flanges of the beam in the fabricator’s workshop and bolted to the column on site. The end-plate connection has been used extensively since the 1960s. The extended end-plate connections are classified into two types as end-plate either extended on the tension side only or on both the tension and compression sides as shown in Figures 3.6 and 3.7. A typical flush end-plate connection is shown in Figure 3.8. Since some endplate connections are considered as a Type FR construction rather than a Type PR construction in the AISC-LRFD specifications (1994), they have often been used as a means of transferring beam end moment to the column. The extended end-plate connection on both sides is preferred when the connection is subjected to moment reversal such as during severe earthquake loading. While the flush end-plate connection is weaker than the extended end-plate connection, this connection type is often used in roof details. The behavior of the end-plate connection depends on the stiffness of the column flange near the connection. The stiffeners of the column flanges act to prevent flexural deformation, thereby influencing the behavior of the plate and the fasteners.

3.6 Header Plate Connections A header plate connection is made with an end plate whose length is less than the depth of the beam. The end plate is always welded to the beam web (with fillet welds on each side) and is bolted

column extended end-plate

beam

FIGURE 3.6 Extended end-plate connection only on tension side.

76


column extended end-plate

beam

FIGURE 3.7 Extended end-plate connection on both tension and compression sides.

column flush end-plate

beam

FIGURE 3.8 Flush end-plate connection.


77

column

beam

header plate

FIGURE 3.9 Header plate connection.

on site to the column as shown in Figure 3.9. This connection is also called a shear end-plate connection in the AISC-LRFD specifications (1994). The moment-rotation characteristics of these connections are similar to those of double web-angle connections. Accordingly, the header plate connections are used mainly to transfer the reaction of the beam to the column and are classified as Type 2 framing in the AISC-ASD specifications (1989).

References AISC, Load and Resistance Factor Design Specifications for Structural Steel Buildings, 2nd edition, American Institute of Steel Construction, Chicago, 1994. AISC, Allowable Stress Design and Plastic Design Specifications for Structural Steel Buildings, 9th edition, American Institute of Steel Construction, Chicago, 1989. Bell, W. G., Chesson, E., Jr., and Munse, W. H., Static tests of standard riveted and bolted beam-to-column connections, University of Illinois Engineering Experiment Station, College of Engineering. University of Illinois at Urbana-Champaign, 1958. Lewitt, C. W., Chesson, E., Jr., and Munse, W. H., Restraint characteristics of flexible riveted and bolted beamto-column connections, Department of Civil Engineering, University of Illinois, 1966. Rathbun, J. C., Elastic properties of riveted connections, Transactions of ASCE, 101, 524–563, 1936.

4

Modeling of Connections


4.1 General Remarks..................................................................................................................... 79 4.2 Behavior Under Monotonic Loading.................................................................................... 80 Linear Model • Polynomial Model • Exponential Model • Power Model • Bounding Line Model • Ramberg-Osgood Model • Richard-Abbott Model 4.3 Behavior Under Cyclic Loading............................................................................................ 89 Independent Hardening Model • Kinematic Hardening Model • Bounding Surface Model with Internal Variables

References................................................................................................................................. 92

4.1 General Remarks In the conventional analysis and design of steel framework, the behavior of connections is idealized as perfectly rigid or ideally pinned. However, numerous experimental investigations have clearly shown that actual connections behave nonlinearly due to gradual yielding of connection components such as plates and angles, bolts, etc. A beam-to-column connection is generally subjected to axial force, shear force, and bending moment. For most connections, however, the axial and shear deformations are usually small comparing with the flexural deformation. For simplicity, only the rotational deformation of the connection due to flexural action is considered in this book. Typical moment-rotation (M–θr) curves for several commonly used connections are shown in Figure 4.1. In order to incorporate the M–θr curves more systematically and efficiently into a frame analysis computer program, the moment-rotation relationship is usually modeled by using mathematical functions. The connection behavior can be simplified as a set of M–θr relationships. Mathematically, these relations can be expressed in the general form:

M = f(θr)

(4.1)

θr = g(M)

(4.2)

or, inversely:

79

80


M "Rigid"

Extended end-plate Flush end-plate

Top- and seat-angle with double web-angle

column

Top- and seat-angle

θr

beam

M

Header plate Double web-angle Single web-angle "Pinned"

θr

FIGURE 4.1 Typical moment-rotation (M–θr) curves of the beam-to-column connections.

where f and g are some mathematical functions. M is the moment at the connection, and θr is the relative rotation of the connection.

4.2 Behavior Under Monotonic Loading 4.2.1 Linear Model

The linear model (Rathbun, 1936; etc.) utilizes the initial connection stiffness Rki to represent the connection behavior as shown in Figure 4.2a. Although this model is easy to apply the momentrotation behavior, it overestimates the connection stiffness at finite rotation. Tarpy and Cardinal (1981), Melchers and Kaur (1982), and Lui and Chen (1986) also proposed a bilinear model (see Figure 4.2b), in which the initial slope of moment-rotation curve is replaced by a shallower line at a certain transition moment. Razzaq (1983) proposed a piecewise multilinear model (see Figure 4.2c), in which the nonlinear moment-rotation curve is approximated by a series of straight-line segments. Although these linear models are easy to use, the inaccuracies and the jumps in stiffness at the transition points make them undesirable.


81

M

M

θr

a

M

b

θr

M

θr

c

d

θr

FIGURE 4.2 Different mathematical representations for the moment-rotation curve: (a) linear model; (b) bilinear model; (c) multilinear model; (d) nonlinear model.

4.2.2 Polynomial Model

The first mathematical model is proposed by Frye and Morris (1975), which is based on an oddpower polynomial factor to evaluate the moment-rotation behavior of several types of connection. The Frye-Morris model was developed on the basis of a procedure formulated by Sommer (1969). They used the method of least squares to determine the constant of the polynomial. This model is represented by:

θr = C1 ( KM ) + C2 ( KM )3 + C3 ( KM )5

(4.3)

where K is a standardization parameter depending on the geometrical and mechanical properties of the connection, and C1, C2, and C3 are curve-fitting constants. The main drawback of this formulation is that the tangent connection stiffness may become negative at some value of connection moment M. This is physically unacceptable, and the negative stiffness may cause numerical difficulties in the analysis of frame structures if the tangent stiffness formulation is used. Following the procedure of Frye-Morris (1975), Picard et al. (1976) and Altman et al. (1982) developed prediction equations to describe the M–θr curve for strap-angle connections and top- and seat-angle connection with double web angles, respectively. Goverdhan (1983) re-estimated the size parameters in the standardization constant K for flush end-plate connections to get a good agreement with moment-rotation curves obtained from experimental results. The curve-fitting constants

82


C1, C2, and C3 and the standardization constant K for each connection type are summarized in Table 4.1. The size parameters for each type of connection are shown in Figure 4.3.

4.2.3 Exponential Model

Lui and Chen (1986) used an exponential function to curve-fit the experimental M–θr data. This model is a good representation of the monotonic nonlinear connection behavior. However, if there are some sharp changes in slope in the M–θr curve, this model cannot adequately represent it (Wu, 1989). Kishi and Chen (1986) refined the Lui-Chen exponential model to accommodate any sharp changes in slope in the M-θr experimental data (modified exponential model). The Kishi-Chen model can be used instead of the M–θr experimental data. The modified exponential model is represented by a function of the following form:

m   θ   n M = M 0 + ∑ C j 1 − exp  − r   + ∑ Dk θr − θ k H  θr − θ k   2 jα   k =1 j =1 

(

)

(4.4)

where M0 is the initial connection moment, α is a scaling factor for the purpose of numerical stability, Cj and Dk are curve-fitting parameters, θk is the initial rotation of the k-th linear component given from the experimental M–θr curve, and H[θ] is Heaviside’s step function (unity for θ ≥ 0, zero for θ < 0). Using the linear interpolation technique for the original M–θr experimental data, the weight function for each piece of M–θr data is nearly equal. The constants Cj and Dk for the exponential and linear terms of the function are determined by linear regression analysis. The instantaneous connection stiffness Rk at an arbitrary relative rotation |θr| can be evaluated by differentiating Equation 4.4 with respect to |θr|. TABLE 4.1 (a) Curve-fitting constants and standardization constants for Frye-Morris polynomial model (all size parameters are in inches) Connection types

Curve-fitting constants

Standardization constants

Single web-angle connection

C1 = 4.28 × 10

K = d a−2.4 t a−1.81 g 0.15

−3

C2 = 1.45 × 10−9 C3 = 1.51 × 10−16

Double web-angle connection

C1 = 3.66 × 10−4 C2 = 1.15 × 10−6

K = d a−2.4 t a−1.81 g 0.15

C3 = 4.57 × 10−8 Top- and seat-angle with double webangle connection

C1 = 2.23 × 10−5 C2 = 1.85 × 10−8

Top- and seat-angle connection

C1 = 8.46 × 10−4

K = d −1.287 t −1.128 t c−0.415l a−0.694 (g − db 2

C3 = 3.19 × 10−12 C2 = 1.01 × 10

−4

K = d −1.5 t −0.5 l a−0.7 db−1.1

C3 = 1.24 × 10−8 Extended end-plate connection without column stiffeners

C1 = 1.83 × 10−3 C2 = −1.04 × 10

−4

C3 = 6.38 × 10−6

K = d g−2.4 t p−0.4 db−1.5

)

1.350


83

Extended end-plate connection with column stiffeners

C1 = 1.79 × 10−3 C2 = 1.76 × 10−4

Header plate connection

C1 = 5.10 × 10−5

K = d g−2.4 t p−0.6

C3 = 2.04 × 10−4 C2 = 6.20 × 10−10

K = t p−1.6 g 1.6 d p−2.3 tw−0.5

C3 = 2.40 × 10−13 T-stub connection

C1 = 2.10 × 10−4 C2 = 6.20 × 10−6

K = d −1.5 t −0.5 lt−0.7 db−1.1

C3 = −7.60 × 10−9

TABLE 4.1 (b) curve-fitting constants and standardization constants for Frye-Morris polynomial model (all size parameters are in centimeters) Connection types

Curve-fitting constants

Standardization constants


C1 = 1.67 × 10

K = d a−2.4 t a−1.81 g 0.15

−0

C2 = 8.56 × 10

−2

C3 = 1.35 × 10−3 Double web-angle connection

C1 = 1.43 × 10−1 C2 = 6.79 × 10

1

K = d a−2.4 t a−1.81 g 0.15

C3 = 4.09 × 105 Top- and seat-angle with double webangle connection

C1= 1.50 × 10−3 C2 = 5.60 × 10


C1 = 2.59 × 10−1

−3

K = d −1.287 t −1.128 t c−0.415l a−0.694 (g − db 2

C3 = 4.35 × 10−3 C2 = 2.88 × 10

3

K = d −1.5 t −0.5 l a−0.7 db−1.1

C3 = 3.31 × 104 Extended end-plate connection without column stiffeners

C1 = 8.91 × 10−1 C2 = −1.20 × 104

K = d g−2.4 t p−0.4 db−1.5

C3 = 1.75 × 108

Extended end-plate connection with column stiffeners

C1 = 2.60 × 10−1 C2 = 5.36 × 102


C1 = 6.14 × 10−3

K = d g−2.4 t p−0.6

C3 = 1.31 × 107 C2 = 1.08 × 10−3

K = t p−1.6 g 1.6 d p−2.3 tw−0.5

C3 = 6.05 × 10−3 T-stub connection

C1 = 6.42 × 10−2 C2 = 1.77 × 102 C3 = −2.03 × 104

K = d −1.5 t −0.5 lt−0.7 db−1.1

)

1.350

p1 = da

p2 = ta

p 1 = da

p3 = g

p3 = g

p2 = ta

b

a p6 = db (fastener dia.)

p4 = db (fastener dia.)

p4 = la

p2 = t

p3 = la

p2 = t p5 = g

p1 = d

p1 = d

p3 = tc

c

d welded

p3 = db (fastener dia.)

p1 = dg

p 1 = dg

welded

column stiffener

p2 = tp

p2 = tp

f

e

p4 = db (fastener dia.) welded

p4 = tw

p2 = t

p3 = dp

p1 = tp

g

p3 = lt

p1 = d

p2 = g

h

FIGURE 4.3 Size parameters for various connection types of the Frye-Morris polynomial model: (a) single web-angle connection; (b) double web-angle connection; (c) top- and seat-angle connection with double web-angle; (d) top- and seat-angle connection; (e) extended end-plate connection without column stiffener; (f) extended end-plate connection with column stiffener; (g) header plate connection; (h) T-stub connection. 84


85

When the connection is loaded, we obtain the equation as follows:

Rk = Rkt =

dM d θr

θr = θr

Cj

 θ  n  − r  + ∑ Dk H  θr − θ k  exp    2 jα  k =1 j =1 2 jα m

=∑

(4.5)

When connection is unloaded, we have: Rk = Rkt =

dM d θr

m

θr = 0

=∑ j =1

Cj

2 jα

+ Dk H  θ k 

(4.6)

k =1

This model has the following merits:

1. The formulation is relatively simple and straightforward. 2. It can deal with connection loading and unloading for the full range of relative rotation in a second-order structural analysis with secant connection stiffness. 3. The abrupt changes in the connection stiffness among the sampling data is only generated from inherent experimental characteristics.

The curve-fitting and tangent connection stiffness values from the experimental data examined are calculated with m = 6 in Equations 4.4 through 4.6. The comparison between the Chen-Lui exponential model (1985) and the modified exponential model for the numerical example of the test data, including a linear component, is shown in Figure 4.4. Yee and Melchers (1986) proposed a four-parameter exponential model:

(

)

  Rki − K p + Cθr θr     + K pθr M = M p 1 − exp  − Mp    

(4.7)

where Mp is the plastic moment capacity, Rki is the initial connection stiffness, Kp is the strainhardening stiffness, and C is a constant controlling the slope of the curve.

M

Experiment Exponential model Modified exponential model

θr

FIGURE 4.4 Comparison between results using exponential and modified exponential models for M–θr data including a linear term.

86


As with the other exponential model, the Wu-Chen model (1990) proposed a three-parameter exponential model in the form of:  θ  M = n ln  1 + r  Mu  θ0 

(4.8)

where Mu is an idealized elastic-plastic mechanism moment, θ0 is a reference rotation (= Mu/Rki), Rki is the initial connection stiffness, and n is the shape parameter, which is determined empirically from test data.

4.2.4 Power Model

Several power models have been developed for the different types of connection. Two or three parameters are required in their functions. A two-parameter model (Batho and Lash, 1936; Krishnamurthy et al., 1979) has the simple form:

θr = aM b

(4.9)

where a and b are two curve-fitting parameters with the condition a > 0 and b > 1. Colson and Louveau (1983) introduced a three-parameter power model function as:

θr =

M 1 Rki 1 − M M u

(

n

)

(4.10)

where Rki is the initial connection stiffness, Mu is the ultimate capacity of connection moment, and n is the shape parameter. Kishi and Chen (1987a, 1987b) proposed a similar model removing the strain-hardening stiffness of the Richard-Abott model (Richard and Abott, 1975):

θr =

M   M  Rki 1 −     M u 

n

  

1/ n

or

M=

Rkiθr   θ  n  1 +  r     θ 0  

1/ n

(4.11a, b)

where Rki, Mu, and n are the same as those defined in the previous Equation 4.10, and θ0 is a reference plastic rotation (= Mu /Rki). Equation 4.11 has the shape shown in Figure 4.5. From this figure, it is seen that the larger the power index n, the steeper the curve. The shape parameter n can be determined using the method of least squares for the differences between the predicted moments and the experimental test data (Kishi et al., 1993, 1995). This power model is an effective tool for designers to execute the second-order nonlinear structural analysis quickly and accurately. This is because the tangent connection stiffness Rk and relative rotation θr can be determined directly from Equation 4.11 without iteration, in which the tangent connection stiffness Rk in Equation 4.11 is:

Rk =

Rki dM = ( n +1)/ n n dθr    θr   1 +      θ 0  

(4.12)


87

M

M = Rki θ r n=

n = n3 n = n2

8

Mu

n = n1

n1 < n2 < n3 M= Rki

Rki θ r 1+ θ r θ0

n 1/ n

θr

θ 0 = Mu / Rki

FIGURE 4.5 Three-parameter power model.

4.2.5 Bounding Line Model

Al-bermani et al. (1994) and Zhu et al. (1995) have proposed a bounding line model as shown in Figure 4.6. It requires four parameters and the concept of this model is to divide the curve into three segments, in which the first and third segments are linear elastic and plastic portions, respectively, and the second segment is a smooth transition portion. The form of this model is represented as:

 Rθ  ki r  M − m1 R − Rki M =  Rki + M c − M y kp   R θ  kp r

(

M < m1

)

m1 ≤ M < m2

(4.13)

M ≥ m2 m where m1 = My + Rkpθr, m2 = Mc + Rkpθr, Rki and Rkp are the initial connection stiffness and the bounding connection stiffness, respectively, My is the yielding connection moment, and Mc is the bounding connection moment.

4.2.6 Ramberg-Osgood Model

The Ramberg-Osgood model was originally proposed for nonlinear stress-strain relationships by Ramberg and Osgood (1943) and then standardized by Ang and Morris (1984). The M–θr curve of this model is represented as: n −1 θr KM   KM   (4.14) = 1 +   θ 0 ( KM )0   ( KM )0   where (KM)0 and θ0 are constants defining the position of the intersection point A (see Figure 4.7), n is a parameter defining the sharpness of the curve, and K is a dimensionless factor depending on the connection type and geometry.

88


M m2

Mc

1 1

m1

My

R ki

FIGURE 4.6 Bounding line model.

R kp R kp

θr

M n = n1 n = n2 n = n3

A

(KM)0

n1 < n2 < n3 Rki FIGURE 4.7 Ramberg-Osgood model.

θ0 =

2θ0

θ0

(KM)0 R ki

θr

4.2.7 Richard-Abbott Model

The four-parameter power model is proposed by Richard and Abbott (1975) for modeling elasticplastic stress-strain relation as shown in Figure 4.8. In the virgin loading path, the M–θr curve is written by the following expression:

M=

(R

ki

)

− Rkp θr

n   θr   1 +      θ 0  

1

n

+ Rkpθr

(4.15)

where Rki is the initial connection stiffness, Rkp is the strain-hardening connection stiffness, n is the shape parameter, θ0 is the reference relative rotation [= M0/(Rki − Rkp)], and M0 is the reference connection moment.


89

M

M= Rki θ r

M0

8

n=

R kp 1

n = n3 n = n2 n = n1

n1 < n2 < n3

Rki

θr

θ 0 =M0 /(Rki - Rkp) FIGURE 4.8 Richard-Abbott model.

4.3 Behavior Under Cyclic Loading 4.3.1 Independent Hardening Model

The independent hardening model (Chen and Saleeb, 1982) is a simple method for representing behavior under cyclic loading. The characteristics of connection behavior are assumed to be unchanged following the virgin M–θr curve under the loading and reloading conditions. Since the loops of the M–θr relation in each cycle are independent, no hardening effect is considered. The cyclic M–θr relation based on this model is schematically shown in Figure 4.9. In the case of

M

R ki

1 e

d

1

Rki

a

1

R ki

b

c FIGURE 4.9 Independent hardening model.

θr

90


unloading from the point a on the initial loading curve, the connection unloads linearly down to M = 0 with the initial connection stiffness Rki. When the sign of the connection moment M changes at the point b in the unloading process, the connection enters into the reverse loading process. In this case, the connection behavior (excluding the residual plastic rotation) resulting from the previous loading process is assumed to coincide with that of the virgin connections under monotonic loading.

4.3.2 Kinematic Hardening Model

The kinematic hardening model is a modified independent hardening model taking into account the effect of material hardening. The behavior of this connection model is illustrated in Figure 4.10, which is represented by the hardening line with the slope Rb. In the case of reversal unloading, the path of the M–θr curve moves along the line with the slope of the initial connection stiffness Rki (i.e., for line ab or cd) until it reaches the hardening line. For further reversal unloading, the path follows the virgin nonlinear M–θr curve of the connection under the monotonic loading (i.e., for line bc or de). If the hardening line has a zero slope (i.e., Rb = 0), the kinematic hardening model is exactly the same as the independent hardening model.

4.3.3 Bounding Surface Model with Internal Variables

The previously mentioned independent and kinematic hardening models are simple to use in frame analysis. Although these models can handle the M–θr relation under one cycle loading, unloading, and reversal loading, the connection behavior for a repetition of this loading cycle cannot be expressed with acceptable accuracy. As shown in Figure 4.11, one problem associated with the independent and kinematic hardening models is that the M–θr relation is completely different depending on whether the connection is reloaded from the region between a and b or from

M e

1 Rb 1 Rki d 1

b

a

1

Rki

θr

1 Rb Rki

c FIGURE 4.10 Kinematic hardening model.

1 Rb


91

M a 1 Rki b

a

θr

c

M a 1 Rki

b

b

θr

c

FIGURE 4.11 Problems associated with the kinematic hardening model: (a) reloading from the region between a and b; (b) reloading from the region between b and c.

the region between b and c. To overcome this deficiency, a bounding surface model with internal variables (Dafalias and Popov, 1976) may be used (Cook, 1983; Goto et al., 1991, 1993). In this model, the M–θr relation is defined in the incremental form:

∆M = Rkt ∆θr

(4.16)

where Rkt is the tangent stiffness of the connections. The tangent connection stiffness Rkt is represented in terms of the initial connection stiffness Rki and the plastic tangent connection stiffness Rkp as: Rkt Rkp Rkt = Rki + Rkp (4.17)

92


M 1 Rb

g line boundin a

δ δin

δ

1

Rkp

1

δin

Rkp

Rkp

1

δ in

p

θr

δ

b

1 Rb

c FIGURE 4.12 Bounding surface model.

The plastic tangent connection stiffness Rkp is represented by using the plastic internal variables δ and δin

Rkp = Rb + h

δ δ in − δ

(4.18)

where h is the hardening shape parameter, Rb is the slope of the bounding line, δ is the distance of the current moment state from the corresponding bound, and δin is the value of δ at the initiation of each loading process. These quantities are schematically shown in Figure 4.12 using the moment-plastic rotation (M–θrp) curve.

References Al-Bermani, F. G. A, Li B., Zhu K., and Kitipornchai S., Cyclic and seismic response of flexibly jointed frames, Engineering Structures, 16(4), 249–255, 1994. Altman, W. G., Azizinamini, A., Bradburn, J. H., and Radziminski, J. B., Moment-rotation characteristics of semi-rigid steel beam-column connections, Final Report, South Carolina University, Columbia. Department of Civil Engineering, SC, 1982. Ang, K. M. and Morris, G. A., Analysis of three-dimensional frames with flexible beam-column connections, Canadian Journal of Civil Engineering, 11, 245–254, 1984. Batho, C. and Lash, S. D., Further investigations on beam and stanchions connections, Including connections encased in concrete; Together with laboratory investigations on a full-scale steel frame, Final report of the Steel Structures Research Committee, Department of Scientific and Industrial Research, His Majesty’s Stationery Office, London, 1936. Chen, W. F. and Lui, E. M., Column with end restraint and bending in load and resistance factor design, AISC Engineering Journal, 22(4), 105–132, 1985. Chen, W. F. and Saleeb, A. F., Uniaxial behavior and modeling in plasticity, Structural Engineering Report No. CE-STR-82–35, School of Civil Engineering, Purdue University, W. Lafayette, IN, 1982.


93

Colson, A. and Louveau, J. M., Connections incidence on the inelastic behavior of steel structures, Proceedings of the Euromech Colloquium, 174, 1983. Cook, N. E., Strength of flexibly-connected steel frames under load histories, Thesis presented to University of Colorado, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Boulder, CO, 1983. Dafalias, Y. F. and Popov, E. P., Plastic internal variables formalism of cyclic plasticity, Series E-Journal of Applied Mechanics, Transactions, ASME, 43, 645–651, 1976. Frye, M. J. and Morris, G. A., Analysis of flexibly connected steel frames, Canadian Journal of Civil Engineering, 2(3), 280–291, 1975. Goto, Y., Suzuki, S., and Chen, W. F., Stability behaviour of semi-rigid sway frames, Engineering Structures, 15(3), 209–219, 1993. Goto, Y., Suzuki, S., and Chen, W. F., Analysis of critical behavior of semi-rigid frames with or without load history in connections. International Journal of Solids and Structures, 27(4), 467–483, 1991. Goverdhan, A. V., A collection of experimental moment-rotation curves and evaluation of prediction equations for semi-rigid connections, Thesis presented to Vanderbilt University, in partial fulfillment of the requirements for the degree of Master of Science, Nashville, TN, 1983. Kishi, N., Hasan, R., Chen, W. F., and Goto, Y., Power model for semi-rigid connections, Steel Structures, Journal of Singapore Structural Steel Society, 5(1), 37–48, 1995. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K. G., Design aid of semi-rigid connections for frame analysis, AISC Engineering Journal, 30(3), 90–107, 1993. Kishi, N., Chen, W. F., Matsuoka, K. G., and Nomachi, S. G., Moment-rotation relation of top- and seat-angle with double web-angle connections, Proceedings of the State-of-the-Art Workshop on Connections and the Behavior, Strength and Design of Steel Structures, R. Bjorhovde, J. Brozzetti, and A. Colson, eds., Ecole Normale Superieure, Cachan, France, May 25–27, 1987a. Kishi, N., Chen, W. F., Matsuoka, K. G., and Nomachi, S. G., Moment-rotation relation of single/double web-angle connections, Proceedings of the State-of-the-Art Workshop on Connections and the Behavior, Strength and Design of Steel Structures, R. Bjorhovde, J. Brozzetti, and A. Colson, eds., Ecole Normale Superieure de Cachan, France, May 25–27, 1987b. Kishi, N. and Chen, W. F., Database of steel beam-to-column connections, Structural Engineering Report No. CE-STR-86-26, School of Civil Engineering, Purdue University, West Lafayette, IN, 1986. Krishnamurthy, N., Huang, H. T., Jefferey, P. K., and Avery, L. K., Analytical M-θ curves for end-plate connections, Journal of the Structural Division, ASCE, 105(1), 133–145, 1979. Lui, E. M. and Chen, W. F., Analysis and behavior of flexibly-jointed frames, Engineering Structures, 8(2), 107–118, 1986. Melchers, R. E. and Kaur, D., Behaviour of frames with flexible joints, Proceedings of 8th Australian Conference Mechanical of Structural Materials, Newcastle, Australia, 27.1–27.5, 1982. Picard, A., Giroux, Y. M., and Brun, P., Analysis of flexibly connected steel frames: Discussion by Frye, M. J. and Morris, G. A., Canadian Journal of Civil Engineering, 3(2), 350–352, 1976. Ramberg, W. and Osgood, W. R., Description of stress-strain curves by three parameters, National Advisory Committee for Aeronautics, Washington, DC, Technical notes No.902, 1943. Rathbun, J. C., Elastic properties of riveted connections, Transaction of the ASCE, 101, 524–563, 1936. Razzaq, Z., End restraint effect on steel column strength, Journal of Structural Engineering, ASCE, 109(2), 314–334, 1983. Richard, R. M. and Abbott, B. J., Versatile elastic-plastic stress-strain formula, Journal of the Engineering Mechanics Division, ASCE, 101(4), 511–515, 1975. Sommer W. H., Behaviour of welded header-plate connections, Thesis presented to University of Toronto, in partial fulfillment of the requirements for the degree of Master of Applied Science, Toronto, Canada, 1969. Tarpy, T. S. and Cardinal, J. W., Behavior of semi-rigid beam-to-column end plate connections, Proceedings of the International Conference: Joints in Structural Steelwork, Teesside Polytechnic, Middlesbrough, Cleveland, UK, 2.3–2.25, 1981. Wu, F. S. and Chen, W. F., A design model for semi-rigid connections, Engineering Structures, 12(2), 88–97, 1990.

94


Wu, F. S., Semi-rigid connections in steel frames, Thesis presented to Purdue University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, West Lafayette, IN, 1989. Yee, Y. L. and Melchers, R. E., Moment-rotation curves for bolted connections, Journal of Structural Engineering, ASCE, 112(3), 615–635, 1986. Zhu, K., Al-Bermani, F. G. A., Kitipornchai, S., and Li, B., Dynamic response of flexibly jointed frames, Engineering Structures, 17(8), 575–580, 1995.

5

Steel Connection Database


5.1 General Remarks..................................................................................................................... 95 5.2 Parameter Definition for Connection Type....................................................................... 100 Single Web-angle Connections/Single Plate Connections • Double Web-angle Connections • Top- and Seat-angle with Double Web-angle Connections • Topand Seat-angle Connections • Extended End-plate Connections • Flush End-plate Connections • Header plate Connections 5.3 Steel Connection Databank Program................................................................................. 129 Outline of SCDB • User Manual for SCDB Program • Examples 5.4 Web Site of Connections...................................................................................................... 132

5.1 General Remarks Conventional analysis and design of steel frameworks are performed using the assumption that the connections are either fully rigid or ideally pinned. The assumption of the fully rigid connection implies that no relative rotation of connection occurs and the end moment of the beam is completely transferred to the column. On the other hand, the pinned connection implies that no restraint on the rotation of connection exists and the connection moment is always zero. However, it is recognized that actual beam-to-column connections always provide some rigidity. The primary distortion of a steel beam-to-column connection is its rotational deformation θr, caused by the in-plane bending moment M (Figure 5.1). The effect of this connection deformation has a destabilizing effect on the frame stability since additional drift will occur because of the decrease in the effective stiffness of the members to which the connections are attached. An increased frame drift will intensify the P-Δ effect, affecting the overall stability of the frame. Thus, the nonlinear characteristics of the beam-to-column connection play a very important role in frame stability. New design method has shifted from the allowable stress design (ASD) method to a limit-state design method such as the AISC load and resistance factor design (LRFD) specifications (AISC, 1994). The limit-state design specifications refer to a more sophisticated method of analysis than the allowable stress design specifications. For example, AISC-LRFD 95

96


θr

Column Beam

M

FIGURE 5.1 Rotational deformation of a connection.

specifications require that the limit state of the structural stability corresponds to the analysis method used for design as follows:

1. When structures are designed on the basis of plastic analysis, the required flexural strength Mu should be determined from a second-order plastic analysis. 2. When designed on the basis of elastic analysis, Mu for beam-columns, connections, and connected members should be determined from a second-order elastic analysis or approximate second-order analysis by means of the first-order elastic analysis method with B1/B2 amplification factors.

While two types of construction are defined in the specifications—fully restrained (FR) construction and partially restrained (PR) construction—the guidelines for the design of the PR construction are not given since it is difficult to evaluate the actual restraint of the semi-rigid connections used in engineering practice. To establish the guideline for design of the PR frames, it is necessary to know the M–θr behavior of the actual beam-to-column connections and to formulate the appropriate M–θr model for use in the design and analysis of PR frames. In recent years, several researchers have published papers discussing the influences of connection rigidity on steel frame structures for all connection types. For example, Goverdhan (1983) collected much of the available test data on momentrotation characteristics and tried to formulate a prediction equation for each type of connection. Nethercot (1985) conducted an extensive literature survey for steel beam-to-column connection


97

test data and their corresponding M–θr curve representations for the period 1915–1985. Kishi and Chen (1986b) and Chen and Kishi (1989) also collected experimental test data published from 1936 to 1985 and compiled a database. After that, Kishi and his colleagues revised the database appending 93 experimental data for the period 1986–1998. Komuro and Kishi (2009) upgraded the connection database including the SCDB program. The connection data compiled in the database have now reached 486. The aim of this chapter is to provide moment-rotation characteristics and corresponding parameters of the semi-rigid beam-to-column connections used frequently in steel construction. Based on the experimental test data collected by Kishi-Chen, a database on steel beam-to-column connections was developed at Purdue University Computer Center and then revised by appending newly performed experimental results. To control this database systematically, the Steel Connection Data Bank (SCDB) program has been developed (Kishi and Chen, 1986a). The SCDB program provides seven main functions including routines for tabulating the experimental test data and the tangent connection stiffness evaluated by using some prediction equations. Three prediction equations including the Frye-Morris model, modified exponential model, and threeparameter power model were chosen and installed in the program. Here, the program has been revised by appending a units conversion routine from the customary U.S. units to SI units. The literature survey encompassed experimental data published from 1936 (Rathbun) to 2007 (Sato et al.), on riveted, bolted, and welded connections. All 486 experimental data collected so far are classified into seven types as shown in Table 5.1. The references and number of experimental data of each connection type are listed in Table 5.2. These experimental data with the SCDB program are installed on the J. Ross Web site (http://www.jrosspub.com/wav/). The items for each experimental data registered in the database are:

1. 2. 3. 4. 5. 6.

Connection type and fastening mode Author, test I.D., and tested country The material properties and size of fasteners The material strength of the connection angles and plate All parameters used in beam-to-column connection Moment-rotation test data

Numerical values registered in the database were standardized in the customary U.S. units by executing a subprogram as the pre-processor. The connection type is classified as shown in Table 5.1, and the fastening mode is classified as shown in Table 5.3. The notations of the major parameters for each connection type are identified in the next section. TABLE 5.1 Connection types Type No.

Connection type

1


2

Double web-angle connection

3

Top- and seat-angle connection with double web-angle

4


5

Extended end-plate connection

6

Flush end-plate connection

7


98


TABLE 5.2 Authors and numbers of experimental M–θr curves for each connection type Number of tests

Connection type

Reference (author, year)

Single web-angle and single plate connections

S. L. Lipson (1968)

30

L. E. Thompson et al. (1970)

12

S. L. Lipson et al. (1977)

8

Double web-angle connections

Top- and seat-angle with double web-angle connections

Top- and seat-angle connections

Extended end-plate connections

R. M. Richard et al. (1982)

4

J. C. Rathbun (1936)

7

W. G. Bell et al. (1958)

4

C. W. Lewitt et al. (1966)

6

W. H. Sommer (1969)

4


48

B. Bose (1981)

1

J. B. Davison et al. (1987)

2

J.G. Yang and G.Y. Lee (2007)

3


2

A. Azizinamini et al. (1985)

20

C. W. Roeder et al. (1996)

1

A. S. Elnashai et al. (1998)

1

Z. Fu et al. (1998)

4

L. Calado et al. (2000)

3

M. Komuro et al. (2002)

2


3

R. A. Hechtman and B. G. Johnston (1947)

12

S. M. Maxwell et al. (1981)

12

M. J. Marley (1982)

26


1

A. Azizinamini (1985)

2

W. L. Harper, Jr. (1990)

1

J. B. Mander et al. (1994)

4

C. Bernuzzi et al. (1996)

1

N. Kubo et al. (1999)

5


1

Y. Sato et al. (2007)

6

L. G. Johnson et al. (1960)

1

A. N. Sherbourne (1961)

5

J. R. Bailey (1970)

26

J. O. Surtees and A. P. Mann (1970)

6

J. A. Packer and L. J. Morris (1977)

3

S. A. Ioannides (1978)

6

R. J. Dews (1979)

3 (Continues)


99

TABLE 5.2 (Continued) Extended end-plate connections (Continued)

Flush end-plate connections

Header plate connections

P. Grundy et al. (1980) N. D. Johnstone and W. R. Walpole (1981)

8

A. Mazroi (1983, 1984)

24

Y. L. Yee (1984)

16

D. B. Moore and P. A. C. Sims (1986)

2


1

R. Zandonini and P. Zanon (1987)

9

L. F. L. Ribeiro et al. (1998)

24

B. Bose et al. (1996)

9

L.R.O. Lima (2003)

7

A. M. Girão Coelho (2004, 2007)

11

J. M. Cabrero and E. Bayo (2007)

2

G. Shi et al. (2007)

1

J. R. Ostrander (1970)

24

J. Phillips and J. A. Packer (1981)

5

P. Zoetemeijer (1981)

7


3


1


9

N. D. Brown and D. Anderson (2001)

1

A.W. Thomson and B.M. Broderick (2002)

3

A. M. Girao Coelho and F. S. K. Bijlaard (2007)

4


1

W. H. Sommer (1969)

20


1

A. K. Aggarwal (1990)

5

TABLE 5.3 Fastening mode patterns Pattern No.

2

Fastening mode pattern

1

All riveted

2

All bolted

3

Riveted-to-beam and bolted-to-column

4

Bolted-to-beam and riveted-to-column

5

Riveted-to-beam and welded-to-column

6

Bolted-to-beam and welded-to-column

7

Welded-to-beam and riveted-to-column

8

Welded-to-beam and bolted-to-column

9

All riveted without column stiffener

10

All riveted with column stiffener

11

All bolted without column stiffener

12

All bolted with column stiffener

100


5.2 Parameter Definition for Connection Type 5.2.1 Single Web-angle Connections/Single Plate Connections

Collected experimental moment-rotation data for a single web-angle with bolted beam-to-column connections are tabulated in Table 5.4. Single plate connections and single web-angle connections bolted to the beam and welded to the column are tabulated in Table 5.5. The notations for major parameters of these types of connections as shown in Figures 5.2 and 5.3 are identified as: lp Angle height lu Distance from the top edge of the angle to the tension flange of the beam ll Distance from the bottom edge of the angle to the compression flange of the beam ta Angle thickness gb Distance from the angle’s heel to the center of the fastener holes in the leg adjacent to the beam web face gc Distance from the angle’s heel to the center of the fastener holes in the leg adjacent to the column face cu Distance from the center of the upper fastener holes to the top edge of the angle in the beam web cl Distance from the center of the lower fastener holes to the bottom edge of the angle in the beam web pb Distance between two rows of fasteners in the beam web pc Distance between two rows of fasteners in the column qb Distance between two lines of fasteners in the beam web qc Distance between two lines of fasteners in the column nb Total number of fasteners in the beam nc Total number of fasteners in the column TABLE 5.4 Collected test data for single web-angle bolted beam-to-column connections No. Author

Test id. Angle

lp (in)

gc (in)

gb (in)

pc db (in) (in)

nc

nb

1

S. L. Lipson (1968) AA-2/1

4 × 3.5 × 1/4

5.5

2.56 2.25 3.0 3/4 1 × 2 1 × 2

2

AA-2/2

4 × 3.5 × 1/4

5.5

2.56 2.25 3.0 3/4 1 × 2 1 × 2

3

AA-3/1

4 × 3.5 × 1/4

8.5

2.56 2.25 3.0 3/4 1 × 3 1 × 3

4

AA-3/2

4 × 3.5 × 1/4

8.5

2.56 2.25 3.0 3/4 1 × 3 1 × 3

5

AA-4/1

4 × 3.5 × 1/4

11.5 2.56 2.25 3.0 3/4 1 × 4 1 × 4

6

AA-4/2

4 × 3.5 × 1/4

11.5 2.56 2.25 3.0 3/4 1 × 4 1 × 4

7

AA-5/1

4 × 3.5 × 1/4

14.5 2.56 2.25 3.0 3/4 1 × 5 1 × 5

8

AA-5/2

4 × 3.5 × 1/4

14.5 2.56 2.25 3.0 3/4 1 × 5 1 × 5

9

AA-6/1

4 × 3.5 × 1/4

17.5 2.56 2.25 3.0 3/4 1 × 6 1 × 6

10

AA-6/2

4 × 3.5 × 1/4

17.5 2.56 2.25 3.0 3/4 1 × 6 1 × 6

11

BB-4/1

4 × 3.5 × 5/16 11.5 2.56 2.25 3.0 3/4 1 × 4 1 × 4

12

BB-4/2

4 × 3.5 × 5/16 11.5 2.56 2.25 3.0 3/4 1 × 4 1 × 4

13

B2-4

4 × 3.5 × 5/16 11.5 2.56 2.25 3.0 3/4 1 × 4 1 × 4

14

B3-4

4 × 3.5 × 5/16 11.5 2.56 2.25 3.0 3/4 1 × 4 1 × 4

15

C-4

5 × 3.5 × 5/16 11.5 1.94 2.25 3.0 3/4 1 × 4 1 × 4

16

D-4

5 × 3.5 × 5/16 11.5 1.94 3.25 3.0 3/4 1 × 4 1 × 4


101

TABLE 5.5 Collected test data for single web-angle bolted beam and welded to column connections No.

Author

Test id.

Angle

lp (in)

gb (in)

db (in)

1

S. L. Lipson (1968)

P1-2/1

—

5.5

2.50

3/4

1×2

P1-2/2

—

5.5

2.50

3/4

1×2

3

P1-3/1

—

8.5

2.50

3/4

1×3

4

P1-3/2

—

8.5

2.50

3/4

1×3

5

P1-4/1

—

11.5

2.50

3/4

1×4

6

P1-4/2

—

11.5

2.50

3/4

1×4

7

P1-5/1

—

14.5

2.50

3/4

1×5

8

P1-5/2

—

14.5

2.50

3/4

1×5

9

P1-6/1

—

17.5

2.50

3/4

1×6

10

P1-6/2

—

17.5

2.50

3/4

1×6

11

G-2/1

4 × 3.5 × 5/16

4.75

2.50

3/4

1×2

12

G-3/1

4 × 3.5 × 5/16

8.0

2.50

3/4

1×3

13

G-4/1

4 × 3.5 × 5/16

12.0

2.50

3/4

1×4

14

G-5/1

4 × 3.5 × 5/16

14.5

2.50

3/4

1×5

A1-5

4 × 3 × 3/8

14.5

2.50

3/4

1×5

2

15 16

S. L. Lipson et al. (1977)

nb

A1-6

4 × 3 × 3/8

17.5

2.50

3/4

1×6

17

A1-7

4 × 3 × 3/8

20.5

2.50

3/4

1×7

18

A1-8

4 × 3 × 3/8

23.5

2.50

3/4

1×8

19

A1-9

4 × 3 × 3/8

26.5

2.50

3/4

1×9

20

A1-10

4 × 3 × 3/8

29.5

2.50

3/4

1 × 10

21

A1-11

4 × 3 × 3/8

32.5

2.50

3/4

1 × 11

A1-12

4 × 3 × 3/8

32.5

2.50

3/4

1 × 12

F-1 alt

—

11.5

2.25

3/4

2×—

22 23 24


F-1 alt

—

11.5

2.25

3/4

2×—

25

G-1 alt

—

11.5

2.25

3/4

2×—

26

G-1 alt

—

11.5

2.25

3/4

2×—

27

H-1 alt

—

11.5

2.25

3/4

2×—

28

H-1 alt

—

11.5

2.25

3/4

2×—

29

F-2-1 alt

—

11.5

2.25

3/4

2×—

30

F-2-1 alt

—

11.5

2.25

3/4

2×—

31

F-2-2 alt

—

11.5

2.25

3/4

2×—

32

F-2-2 alt

—

11.5

2.25

3/4

2×—

33

F-2-3 alt

—

11.5

2.25

3/4

2×—

F-2-3 alt

—

11.5

2.25

3/4

2×—

RGKL2

—

6.0

—

3/4

1×2

34 35 36

R. M. Richard et al. (1982)

RGKL2

—

9.0

—

3/4

1×3

37

RGKL2

—

15.0

—

3/4

1×5

38

RGKL2

—

21.5

—

7/8

1×7

102


column

gb

ta

lu cu pb pb pb lp pb cl qb ll

gc beam

pc pc pc pc qc

FIGURE 5.2 Size parameters for single web-angle connection.

column

gb lu cu pb pb pb lp pb cl qb ll

beam

Welded

FIGURE 5.3 Size parameters for single plate connection.


103

5.2.2 Double Web-angle Connections

A total of 75 experimental data have been collected here. Collected experimental moment-rotation data for double web-angle connections are tabulated in Table 5.6. The notations for major parameters of this connection type as shown in Figure 5.4 are identified as: lp lu ll ta gb gc cu cl pb pc q b qc nb nc

Angle height Distance from the top edge of the angle to the tension flange of the beam Distance from the bottom edge of the angle to the compression flange of the beam Angle thickness Distance from the angle’s heel to the center of the fastener holes in the leg adjacent to the beam web face Distance from the angle’s heel to the center of the fastener holes in the leg adjacent to the column face Distance from the center of the upper fastener holes to the top edge of the angle in the beam web Distance from the center of the lower fastener holes to the bottom edge of the angle in the beam web Distance between two rows of fasteners in the beam web Distance between two rows of fasteners in the column Distance between two lines of fasteners in the beam web Distance between two lines of fasteners in the column Total number of fasteners in the beam Total number of fasteners in the column

TABLE 5.6 Collected test data for double web-angle connections gb (in)

pc (in)

6 × 4 × 3/8

2.50 2.63 3.50

—

6 × 4 × 3/8

6.00 2.63 3.50 3.00 7/8˝ 1 × 2 2 × 2

No. Author

Test id.

Angle

1

A-1 A-2

2 3


lp (in)

gc (in)

db

nc

nb

7/8˝ 1 × 1 2 × 1

A-3

6 × 6 × 3/8

6.00 3.63 3.50 3.00 7/8˝ 2 × 2 2 × 2

4

A-4

4 × 3 1/2 × 3/8

9.00 2.56 2.25 3.00 7/8˝ 1 × 3 1 × 3

5

A-5

6 × 6 × 3/8

9.00 3.56 3.50 3.00 7/8˝ 2 × 3 2 × 3

6

A-6

4 × 3 1/2 × 3/8

15.00 2.50 2.25 3.00 7/8˝ 1 × 5 1 × 5

A-7

7 8 9 10 11 12 13

6 × 6 × 3/8

15.00 3.50 3.50 3.00 7/8˝ 2 × 5 2 × 5

W. G. Bell FK-4A et al. (1958) FK-4B

6 × 4 × 3/8

11.50 2.57 4.50 3.00 3/4˝ 1 × 4 2 × 4

6 × 4 × 3/8

11.50 2.57 4.50 3.00 3/4˝ 1 × 4 2 × 4

FK-4C

6 × 4 × 3/8

11.50 2.57 4.50 3.00 3/4˝ 1 × 4 2 × 4

FK-4R

6 × 4 × 3/8

11.50 2.57 4.50 3.00 3/4˝ 1 × 4 2 × 4

C. W. Lewitt FK-3 6 × 4 × 3/8 et al. (1966) FK-4AB-M 6 × 4 × 3/8

8.50 2.63 3.50 3.00 3/4˝ 1 × 3 2 × 3 11.50 2.07 3.50 3.00 3/4˝ 2 × 4 2 × 4

14

FK-4P

6 × 4 × 3/8

11.50 2.07 3.50 3.00 3/4˝ 2 × 4 2 × 4

15

WK-4

6 × 4 × 3/8

11.50 2.57 3.50 3.00 3/4˝ 1 × 4 2 × 4

16

FB-4

6 × 3.5 × 3/8

11.50 2.57 2.25 3.00 3/4˝ 1 × 4 1 × 4

17

FK-5

6 × 4 × 7/16

14.50 2.55 3.50 3.00 3/4˝ 1 × 5 2 × 5 (Continues)

104


TABLE 5.6 (Continued) lp (in)

gc (in)

gb (in)

pc (in)

db

No. Author

Test id.

Angle

18

B. Bose (1981)

B-1

150 × 90 × 15

15.75 2.38 3.54 2.95 M20 1 × 5 2 × –

19

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

21

L. E. A1-1 ALT Thompson A1-1 ALT et al. (1970) A1-2 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

22

A1-2 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

23

A1-3 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

24

A1-3 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

25

B1-1 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

26

B1-1 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

27

B1-2 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

28

B1-2 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

29

B1-3 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

30

B1-3 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

31

D1-1 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

3/4˝ – × – – × 2

32

D1-1 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

3/4˝ – × – – × 2

33

D1-2 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

3/4˝ – × – – × 2

34

D1-2 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

3/4˝ – × – – × 2

35

D1-3 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

3/4˝ – × – – × 2

36

D1-3 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

3/4˝ – × – – × 2

37

E1-1 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

38

E1-1 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

39

E1-2 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

40

E1-2 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

41

E1-3 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

42

E1-3 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

43

A2-1 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2

44

A2-1 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

45

A2-2 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

3/4˝ – × – – × 2 3/4˝ – × – – × 2

46

A2-2 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

47

A2-3 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

48

A2-3 ALT

4 × 3.5 × 5/16

11.50 2.55 2.25

—

49

B2-1 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

50

B2-1 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

51

B2-2 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

52

B2-2 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

53

B2-3 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

54

B2-3 ALT

4 × 3.5 × 5/16

11.50 1.80 2.25

—

55

C2-1 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

20

nc

nb

3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 3/4˝ – × – – × 2 (Continues)


105

TABLE 5.6 (Continued) No. Author 56

Test id.

lp (in)

Angle

gc (in)

gb (in)

pc (in)

db

nc

nb

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

59

C2-1 ALT L. E. Thompson C2-2 ALT et al. (1970) C2-2 ALT (Continued) C2-3 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

60

C2-3 ALT

4 × 3.5 × 1/2

11.50 2.55 2.25

—

3/4˝ – × – – × 2

61

D2-1 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

62

D2-1 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

63

D2-2 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

64

D2-2 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

65

D2-3 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

D2-3 ALT

4 × 3.5 × 1/2

11.50 1.80 2.25

—

3/4˝ – × – – × 2

TEST21

3.5 × 3 × 3/8

9.00 1.83

3.00 3/4˝ 1 × 3

TEST22

3.5 × 3 × 3/8

12.00 1.83

3.00 3/4˝ 1 × 4

TEST23

4 × 3 × 3/8

15.00 2.53

3.00 3/4˝ 1 × 5

TEST24

4 × 3 × 3/8

18.00 2.53

3.00 3/4˝ 1 × 6

57 58

66 67 68 69

W. H. Sommer (1969)

70 71 72 73 74 75

J. B. JT/01B Davison JT/06 et al. (1987) J. G. Yang and G. Y. Lee (2007)

RSA 80 × 60 × 8 6.30 1.38 2.17 3.94 M16 2 × 2 1 × 2 RSA 80 × 60 × 8 6.30 1.38 2.17 3.94 M16 2 × 2 1 × 2

3B-L-7-65 L125 × 75 × 7

8.27 2.56

—

2.76 M20 1 × 3

4B-L-7-65 L125 × 75 × 7

11.02 2.56

—

2.76 M20 1 × 4

5B-L-7-65 L125 × 75 × 7

13.78 2.56

—

2.76 M20 1 × 4

column

gb lu

ta

cu pb pb pb lp pb cl qb ll

gc beam pc pc pc pc qc

FIGURE 5.4 Size parameters for double web-angle connection.

106


5.2.3 Top- and Seat-angle with Double Web-angle Connections

The experimental studies on this connection type were mainly performed by Altman et al. (1982) and Azizinamini et al. (1985) at University of South Carolina. The test program included specimens that were subjected to both cyclic loading and static loading. A total of 33 experimental data has been collected. However, cyclic loading test data are excluded from the database, as listed in Table 5.7. The notations for major parameters of this connection type as shown in Figure 5.5 are as follows: On the web angle: lp lu ll ta gb gc cu cl pb pc q b qc nb nc

Angle height Distance from the top edge of the angle to the tension flange of the beam Distance from the bottom edge of the angle to the compression flange of the beam Web-angle thickness Distance from the angle’s heel to the center of the fastener holes in the leg adjacent to the beam web face Distance from the angle’s heel to the center of the fastener holes in the leg adjacent to the column face Distance from the center of the upper fastener holes to the top edge of the angle in the beam web Distance from the center of the lower fastener holes to the bottom edge of the angle in the beam web Distance between two rows of fasteners in the beam web Distance between two rows of fasteners in the column Distance between two lines of fasteners in the beam web Distance between two lines of fasteners in the column Total number of fasteners in the beam Total number of fasteners in the column

On the top and seat angles: lt tt ls ts gt gtʹ gs gsʹ qt qt2 rt rt2

Width of the top angle along the column Top-angle thickness Width of the seat angle along the column Seat-angle thickness Gage from the top angle’s heel to the center of the fastener holes in the leg seating on the tension-beam flange Gage from the top angle’s heel to the center of the fastener holes in the leg adjacent to the column face Gage from the seat angle’s heel to the center of the fastener holes in the leg under the compression-beam flange Gage from the seat angle’s heel to the center of the fastener holes in the leg adjacent to the column face Distance between two inner lines of fasteners in the leg seating on the tension-beam flange Distance between the outer and inner lines of fasteners in the leg seating on the tensionbeam flange where the number of fastener lines exceeds three Distance between two inner lines of fasteners in the leg adjacent to the column face in the tension side Distance between the outer and inner lines of fasteners in the leg adjacent to the column face in the tension side where the number of fastener lines exceeds three

8S8

8S9

8S10

14S1

14S2

14S3

14S4

14S5

14S6

14S8

14S9

14WS1

14WS2

B-11

8

9

10

11

12

13

14

15

16

17

18

19

20

21

L1

8S7

7

B-12

8S6

6

C.W. Roeder et al. (1996)

8S5

5

23

8S4

4

22

8S3

8S2

8S1

Test id.

3

J.C.Rathbun (1936)

A. Azizinamini et al. (1985)

1

2

Author

No

W14 × 22

W12 × 31.8

W12 × 31.8

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W14 × 38

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

Beam

W10 × 68

—

—

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 96

W12 × 58

W12 × 58

W12 × 58

W12 × 58

W12 × 58

W12 × 58

W12 × 58

W12 × 58

W12 × 58

W12 × 58

Column

TABLE 5.7 Collected test data for top- and seat-angle with double web-angle connections

L5 × 3.5 × 5/8

6 × 6.0 × 3/8 × 14 (top)

6 × 6.0 × 3/8 × 9 (top)

6 × 4.0 × 1/2 × 8.0

6 × 4.0 × 3/8 × 8.0

6 × 4.0 × 1/2 × 8.0

6 × 4.0 × 5/8 × 8.0

6 × 4.0 × 1/2 × 8.0

6 × 4.0 × 3/8 × 8.0

6 × 4.0 × 3/8 × 8.0

6 × 4.0 × 3/8 × 8.0

6 × 4.0 × 1/2 × 8.0

6 × 4.0 × 3/8 × 8.0

6 × 3.5 × 1/2 × 6.0

6 × 3.5 × 3/8 × 6.0

6 × 3.5 × 5/16 × 6.0

6 × 4.0 × 3/8 × 6.0

6 × 4.0 × 5/16 × 6.0

6 × 4.0 × 3/8 × 8.0

6 × 6.0 × 3/8 × 6.0

6 × 3.5 × 5/16 × 8.0

6 × 3.5 × 3/8 × 6.0

6 × 3.5 × 5/16 × 6.0

F. Angle

(Continues)

L3.5 × 3 × 5/16

4 × 3.5 × 3/8 × 9

4 × 3.5 × 3/8 × 9

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 3/8 × 8.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 8.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

4 × 3.5 × 1/4 × 5.5

W. Angle

Steel Connection Database 107

W29-m

W18-m

32

33

BCC10-M

31


BCC9-M

BCC7-M

29

L.Calado et al. (2000)

LM-T15

28

30

LM-P15

LM-P

LM-T

Z. Fu et al. (1998)

25

SRB01

27

A.S. Elnashai et al. (1998)

24

Test id.

26

Author

No

TABLE 5.7 (Continued)

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

IPE300

IPE300

IPE300

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

H250 × 130 × 9 × 9

Beam

—

—

HEB240

HEB160

HEB200

—

—

—

—

H150 × 150 × 7 × 10

Column

L150 × 100 × 12

L150 × 100 × 12

L120 × 120 × 10

L120 × 120 × 10

L120 × 120 × 10

L75 × 75 × 9 × 8.5

L75 × 75 × 9 × 8.5

L75 × 75 × 9 × 8.5

L75 × 75 × 9 × 8.5

L75 × 75 × 9

F. Angle

L90 × 90 × 7

L90 × 90 × 7

L120 × 80 × 10

L120 × 80 × 10

L120 × 80 × 10

L75 × 75 × 9 × 8.5

L75 × 75 × 9 × 8.5

L75 × 75 × 9 × 8.5

L75 × 75 × 9 × 8.5

L75 × 75 × 8

W. Angle



109

qs Distance between two inner lines of fasteners in the leg under the compression-beam flange qs2 Distance between the outer lines and the inner lines of fasteners in the leg under the compression-beam flange where the number of fastener lines exceeds three rs Distance between two inner lines of fasteners in the leg adjacent to the column face in the compression side rs2 Distance between the outer and inner lines of fasteners in the leg adjacent to the column face in the compression side where the number of fastener lines exceeds three pt Distance between two rows of fasteners in the leg seating on the tension-beam flange ptʹ Distance between two rows of fasteners in the leg adjacent to the column face in the tension side ps Distance between two rows of fasteners in the leg under the compression-beam flange psʹ Distance between two rows of fasteners in the leg adjacent to the column face in the compression side nt Total number of fasteners in the tension-beam flange ntʹ Total number of fasteners in the leg adjacent to the column face in the tension side ns Total number of fasteners in the compression-beam flange nsʹ Total number of fasteners in the leg adjacent to the column face in the compression side

column

lt rt

gt

tt

gt' pt ta

cu pb pb cl ps

gb

gc

lu beam

qt

pc lp

pc qs

ll gs'

gs FIGURE 5.5 Size parameters for top- and seat-angle connection with double web-angle.

ts rs ls

110


5.2.4 Top- and Seat-angle Connections

The collected experimental data for this connection type are listed in Table 5.8. A total of 74 experimental data have been collected. The notations for major parameters of this connection type as shown in Figure 5.6 are: lt tt ls ts gt gtʹ gs gsʹ qt qt2 rt rt2 qs qs2 rs rs2 pt ptʹ ps psʹ nt ntʹ ns nsʹ

Width of the top angle along the column Top-angle thickness Width of the seat angle along the column Seat-angle thickness Gage from the top angle’s heel to the center of the fastener holes in the leg seating on the tension-beam flange Gage from the top angle’s heel to the center of the fastener holes in the leg adjacent to the column face Gage from the seat angle’s heel to the center of the fastener holes in the leg under the compression-beam flange Gage from the seat angle’s heel to the center of the fastener holes in the leg adjacent to the column Distance between two inner lines of fasteners in the leg seating on the tension-beam flange Distance between the outer and inner lines of fasteners in the leg seating on the tensionbeam flange where the number of fastener lines exceeds three Distance between two inner lines of fasteners in the leg adjacent to the column face in the tension side Distance between the outer and inner lines of fasteners in the leg adjacent to the column face in the tension side where the number of fastener lines exceeds three Distance between two inner lines of fasteners in the leg under the compression-beam flange Distance between the outer lines and the inner lines of fasteners in the leg under the compression-beam flange where the number of fastener lines exceeds three Distance between two inner lines of fasteners in the leg adjacent to the column face in the compression side Distance between the outer and inner lines of fasteners in the leg adjacent to the column face in the compression side where the number of fastener lines exceeds three Distance between two rows of fasteners in the leg seating on the tension-beam flange Distance between two rows of fasteners in the leg adjacent to the column face in the tension side Distance between two rows of fasteners in the leg under the compression-beam flange Distance between two rows of fasteners in the leg adjacent to the column face in the compression side Total number of fasteners in the tension-beam flange Total number of fasteners in the leg adjacent to the column face in the tension side Total number of fasteners in the compression-beam flange Total number of fasteners in leg adjacent to the column face in the compression side

5.2.5 Extended End-plate Connections

The type of extended end-plate connections includes both cases of extension on the tension and compression sides and extension on the tension side only. Collected experimental moment-rotation

C2-1/4-1

C2-1/4-2

D1-1/4-1

D1-1/4-2

D2-1/4-1

22

23

24

25

A-1/4-1

16

C1-1/4-2

NO 24

15

21

NO 23

14

20

NO 22

13

B-1/4-2

NO 20

12

B-1/4-1

NO 18

11

19

NO 17

10

18

NO 16

9

A-1/4-2

NO 11

8

M. J. Marley (1982)

NO 10

7

17

NO 9

6

NO 5

NO 2

R. A. Hechtman and B. G. Johnston (1947)

4

5

B-10

3

B-8

B-9


1

Test id.

2

Author

No.

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W18 × 47

W18 × 40

W16 × 40

W14 × 34

W12 × 50

W12 × 25

W12 × 25

W18 × 47

W18 × 47

W18 × 47

W18 × 47

W12 × 25

W12 × 31.8

W12 × 31.8

W12 × 1.8

Beam

TABLE 5.8 Collected test data for top- and seat-angle connections

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W12 × 65

W14 × 58

W12 × 65

W12 × 65

W10 × 49

W10 × 49

W10 × 49

W14 × 58

W12 × 65

W12 × 65

W12 × 65

W10 × 49

—

—

—

Column

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

6 × 4 × 5/8 × 12 1/2 (top)

6 × 4 × 5/8 × 10 (top)

6 × 4 × 5/8 × 12 (top)

6 × 4 × 5/8 × 12 (top)

6 × 4 × 1/2 × 8 (top)

6 × 4 × 1/2 × 6 3/4 (top)

6 × 4 × 1/2 × 6 3/4 (top)

6 × 4 × 1/2 × 10 (top)

6 × 4 × 3/4 × 12 (top)

6 × 4 × 5/8 × 12 (top)

6 × 4 × 1/2 × 12 (top)

6 × 4 × 5/8 × 6 3/4 (top)

6 × 6 × 3/8 × 14 (top)

6 × 6 × 3/8 × 8 (top)

6 × 6 × 3/8 × 6 (top)

Angle

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

12.50

10.00

12.00

12.00

8.00

6.75

6.75

10.00

12.00

12.00

12.00

6.75

14.00

8.00

6.00

lt (in)

0.250

0.250

0.250

0.250

0.250

0.250

0.250

0.250

0.250

0.250

0.625

0.625

0.625

0.625

0.500

0.500

0.500

0.500

0.750

0.625

0.500

0.625

0.375

0.375

0.375

(Continues)

—

—

—

—

—

—

—

—

—

—

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

3.50

gt (in) tt (in)


B-1/2-1

B-1/2-2

C1-1/2-1

C1-1/2-2

C2-1/2-1

C2-1/2-2

D1-1/2-1

D1-1/2-2

D2-1/2-1

D2-1/2-2

D3-1/2-1

D3-1/2-2

A1

30

31

32

33

34

35

36

37

38

39

40

41

42

A3

A4

B1

B2

B3

B4

C1

44

45

46

47

48

49

50

A2

A-1/2-1

29

43

D3-1/4-2

D3-1/4-1

D2-1/4-2

Test id.

28

S. M. Maxwell et al. (1981)

M. J. Marley (1982) (Continued)

26

27

Author

No.


457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

Beam

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

W5 × 16

Column

150 × 90 × 15 × 150

150 × 90 × 12 × 200

150 × 90 × 12 × 150

150 × 90 × 12 × 200

150 × 90 × 12 × 150

150 × 90 × 10 × 200

150 × 90 × 10 × 150

150 × 90 × 10 × 200

150 × 90 × 10 × 150

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/2 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

4 × 4 × 1/4 × 5.0

Angle

5.91

7.87

5.91

7.87

5.91

7.87

5.91

7.87

5.91

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

5.00

lt (in)

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

0.591

0.472

0.472

0.472

0.472

0.394

0.394

0.394

0.394

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.500

0.250

0.250

0.250

gt (in) tt (in)


C4

JT/08


A. Azizinamini (1985)

53

54

55

R1_11

TSC/M


N. Kubo et al. (1999)

61

62

63

No.5

No.7

No.9

W00-m


Y. Sato et al. (2007)

65

66

67

68

69

G105

G150

GW60

A40

A90

70

71

72

73

74

G60

No.3

64

No.1

R1_06

60

R1_05

R1_01

J. B. Mander et al. (1994)

59

58

—

W. L. Harper, Jr. (1990) TEST3

57

56

C3

52

—

C2

51

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

H400 × 200 × 8 × 13

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

H250 × 125 × 6 × 9

IPE300

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W8 × 21

W14 × 38

W14 × 38

UB 254 × 102 × 22

457 × 191 × UB

457 × 191 × UB

457 × 191 × UB

—

—

—

—

—

—

—

H175 × 175 × 7.5 × 11

H150 × 150 × 7 × 10

H250 × 250 × 9 × 14

H150 × 150 × 7 × 10

H250 × 250 × 9 × 14

—

W8 × 31

W8 × 31

W8 × 31

W8 × 31

W8 × 24

W12 × 96

W12 × 96

UC152 × 152 × 23

305 × 305 × UC

305 × 305 × UC

305 × 305 × UC

L200 × 150 × 15

L200 × 100 × 15

L200 × 200 × 15

L200 × 200 × 15

L200 × 200 × 15

L200 × 200 × 15

L150 × 100 × 12

L120 × 120 × 8

L120 × 120 × 8

L120 × 120 × 8

L100 × 100 × 10

L100 × 100 × 10

L120 × 120 × 12

6 × 4 × 3/8

6 × 4 × 3/8

6 × 4 × 3/8

6 × 4 × 3/8

6 × 3.5 × 3/8

6 × 4 × 1/2

6 × 4 × 3/8

RSA 80 × 60 × 8 (top)

150 × 90 × 15 × 200

150 × 90 × 15 × 150

150 × 90 × 15 × 200

7.87

7.87

7.87

7.87

7.87

7.87

7.87

5.40

5.41

5.41

5.71

5.72

7.09

6.50

6.50

6.50

6.50

6.00

8.00

8.00

4.76

7.87

5.91

7.87

4.13

4.13

4.13

4.13

4.13

4.13

3.25

2.76

2.77

2.77

2.38

2.34

2.36

3.63

3.63

3.63

3.63

3.00

3.00

3.00

2.17

—

—

—

0.591

0.591

0.591

0.591

0.591

0.591

0.472

0.315

0.307

0.299

0.362

0.366

0.465

0.375

0.375

0.375

0.375

0.375

0.500

0.375

0.315

0.591

0.591

0.591


114


lt rt

column gt

tt

gt' qt

pt beam

qs

ps gs' gs

ts rs ls

FIGURE 5.6 Size parameters for top- and seat-angle connection.

data for extended end-plate connections are tabulated in Table 5.9. This type of connection— apparently used quite often in construction—has been a subject of much experimental work. A total of 166 experimental moment-rotation data have been appended to the original connection database. The notations for major parameters of this connection type as shown in Figure 5.7 are identified as: ct pt li pit pi pic gt gt2 g i gi2 gc

Distance from the tension-side edge of plate to the center of the outer tension-side fastener holes Distance between two rows of tension-side fasteners Distance from the center of the lower tension-side fastener holes to the center of the upper compression-side fasteners holes Distance from the inner row of fasteners on the tension side to the upper row of central fasteners Distance between two inner rows of central fasteners Distance from the inner row of fasteners on the compression side to the lower row of central fasteners Distance between two inner lines of tension-side fasteners Distance from the outer line to the inner line of tension-side fasteners where the number of fastener lines exceeds three Distance between two inner lines of central fasteners Distance from the outer line to the inner line of central fasteners where the number of fastener lines exceeds three Distance between two inner lines of compression-side fasteners

TEST A3-L

TEST A3-R

TEST C1

15

16

17

TEST C5

TEST J1

21

22

24

TEST J3

TEST J2

TEST C4

20

23

TEST C3

19


TEST A2-R

14

TEST C2

TEST A2-L

13

18

TEST A1-R

12


J. R. Bailey (1970)

11

TEST A1-L

TEST A1


10

TEST 1

7

TEST 3

TEST 6

6

TEST 2

TEST 5

5

9

TEST 4

8

TEST 3

4

TEST 2

TEST 1

Test id.

3

R. J. Dews (1979)


1

2

Author

No.

254 × 102 UB 22

254 × 102 UB 22

254 × 102 UB 22

15 × 6 UB 40

15 × 6 UB 40

15 × 6 UB 40

15 × 6 UB 40

12 × 5 UB 25

10 × 4 UB 19

10 × 4 UB 19

10 × 4 UB 17

10 × 4 UB 17

12 × 5 RSJ 32

12 × 5 RSJ 32

15 × 5 RSJ 42

W16 × 26

W14 × 22

W14 × 22

W24 × 55

W18 × 35

W14 × 22

W24 × 55

W18 × 35

W14 × 22

Beam

TABLE 5.9 Collected test data for extended end-plate connections

152 × 152 UC 23

152 × 152 UC 30

152 × 152 UC 37

10 × 10 UC 60

10 × 10 UC 60

10 × 10 UC 60

10 × 10 UC 60

8 × 8 UC 48

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 48

8 × 8 UC 48

8 × 8 UC 35

W10 × 33

W8 × 31

W8 × 31

W14 × 48

W10 × 49

W8 × 35

W14 × 48

W10 × 49

W8 × 35

Column

9.764

9.764

9.764

14.50

14.50

14.50

14.50

11.50

—

—

—

—

—

—

14.50

19.48

17.27

17.16

27.25

21.50

17.25

27.25

21.50

17.25

lp (in)

0.591

0.591

0.591

1.000

1.000

0.750

0.750

0.750

0.850

0.850

0.805

0.805

1.020

1.020

1.250

1.562

0.938

0.969

1.250

1.250

0.875

0.875

0.750

0.625

tp (in)

3.39

3.39

3.39

3.50

3.50

3.50

3.50

3.50

—

—

—

—

—

—

4.00

5.38

5.53

5.50

5.50

5.50

5.50

5.50

5.50

5.50

g (in)

3.82

3.82

3.82

4.50

4.50

4.50

4.50

4.50

4.38

4.38

4.38

4.38

4.50

4.50

3.50

3.75

3.50

3.50

4.00

3.75

3.50

4.00

3.75

3.50

pt (in)

(Continues)

M16

M16

M16

1˝

1˝

1˝

3/4˝

3/4˝

3/4˝

3/4˝

5/8˝

5/8˝

7/8˝

7/8˝

3/4˝

1˝

3/4˝

3/4˝

1˝

7/8˝

3/4˝

1˝

7/8˝

3/4˝

db


P. Grundy et al. (1980)


25

27

TEST 5

J. R. Bailey (1970)

31

32

B4-R

B5-L

B5-R

B6-L

B6-R

B7-L

B7-R

B8-L

B8-R

C9-L

C9-R

C10-L

C10-R

C11-L

C11-R

C12-L

C12-R

33

34

35

36

37

38

39

40

41

42

43

44

45

46

47

48

49

B4-L

TEST B2

L. G. Johnson et al. (1960)

30

TEST B1

TEST A3

TEST A2

T2

T1

Test id.

29

28

26

Author

No.


12 × 6 1/2 UB

12 × 6 1/2 UB

14 × 5 UB 26

14 × 5 UB 26

12 × 5 UB 32

12 × 5 UB 32

8 × 5 1/4 UB

8 × 5 1/4 UB

8 × 5 1/4 UB

8 × 5 1/4 UB

12 × 6 1/2 UB

12 × 6 1/2 UB

14 × 6 3/4 UB

14 × 6 3/4 UB

14 × 5 UB 26

14 × 5 UB 26

12 × 5 UB 32

12 × 5 UB 32

10 × 4 1/2 RSJ

15 × 5 RSJ 42

15 × 5 RSJ 42

15 × 5 RSJ 42

15 × 5 RSJ 42

610 UB 113

610 UB 113

Beam

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 45

8 × 8 UC 35

8 × 8 UC 35

8 × 8 UC 35

8 × 8 UC 35

310 UC 240

310 UC 240

Column

11.69

11.69

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

0.950

0.950

0.825

0.825

0.960

0.960

0.875

0.875

0.920

0.920

1.160

1.160

1.240

1.240

1.000

1.000

1.100

1.100

0.500

—

0.750

9.750

1.000

0.750

1.250

1.250

1.000

tp (in)

14.00

14.00

14.50

14.50

25.78

25.78

lp (in)

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

—

3.50

4.00

4.00

4.00

4.00

3.50

3.50

g (in)

4.38

4.38

4.25

4.25

4.50

4.50

4.50

4.50

4.50

4.50

4.50

4.50

4.63

4.63

4.25

4.25

4.50

4.50

3.75

5.00

5.00

3.50

3.50

3.75

3.75

pt (in)

7/8˝

7/8˝

5/8˝

5/8˝

3/4˝

3/4˝

5/8˝

5/8˝

3/4˝

3/4˝

1˝

1˝

1˝

1˝

3/4˝

3/4˝

7/8˝

7/8˝

3/4˝

7/8˝

7/8˝

3/4˝

3/4˝

7/8˝

7/8˝

db


CF5-U10 × 68

CF5-U14 × 61

CF5-U10 × 49

CF6-U12 × 96

CF6-U14 × 158

72

73

74

75

76

CF4-U12 × 87

69

CF4-U12 × 120

EP8 W

68

CF4-U12 × 106

EP8

67

71

EP7 W

66

70

EP7

65

A. Mazroi (1984)

EP6

EP3

61

EP5

TEST 4-R

60

64

TEST 4-L

59

63

TEST 3-R

58

EP4

TEST 3-L

57

62

TEST 2-R

TEST 2-L

TEST 1-R

56

55

A. Mazroi (1983)

N. D. Johnstone and W. R. Walpole (1981)

53

TEST 1-L

TEST C6

52

54

C13-R


51

C13-L

50

W27 × 114

W27 × 114

W27 × 114

W27 × 114

W27 × 114

W24 × 100

W24 × 100

W24 × 100

W24 × 162

W24 × 162

W24 × 162

W24 × 162

W27 × 114

W27 × 114

W24 × 100

W24 × 100

310 UB 46

310 UB 46

310 UB 46

310 UB 46

310 UB 46

310 UB 46

310 UB 46

310 UB 46

18 × 6 UB 55

14 × 6 3/4 UB

14 × 6 3/4 UB

W14 × 158

W12 × 96

W10 × 49

W14 × 61

W10 × 68

W12 × 120

W12 × 106

W12 × 87

—

—

—

—

—

—

—

—

250 UC 89

250 UC 89

250 UC 89

250 UC 89

250 UC 89

250 UC 89

250 UC 89

250 UC 89

10 × 10 UC 89

8 × 8 UC 40

8 × 8 UC 40

31.25

31.25

30.25

30.25

30.25

26.75

26.75

26.75

29.25

29.25

28.25

28.25

31.25

30.25

26.75

26.75

—

—

—

—

—

—

—

—

16.00

—

—

1.250

1.250

1.000

1.000

1.000

1.000

1.000

1.000

1.750

1.750

1.500

1.500

1.250

1.000

1.000

0.750

0.630

0.630

0.945

0.945

1.260

1.260

1.260

1.260

1.125

1.140

1.140

6.50

6.50

5.50

5.50

5.50

5.50

5.50

5.50

6.50

6.50

5.50

5.50

6.50

5.50

5.50

5.50

5.12

5.12

5.12

5.12

5.51

5.51

5.51

5.51

6.00

—

—

4.93

4.93

3.93

3.93

3.93

3.50

3.50

3.50

5.47

5.47

4.47

4.47

4.93

3.93

3.50

3.50

4.53

4.53

4.02

4.02

7.01

7.01

7.01

7.01

6.00

4.63

4.63

1˝ (Continues)

1˝

1˝

1˝

1˝

7/8˝

7/8˝

7/8˝

1 1/8˝

1 1/8˝

1 1/8˝

1 1/8˝

1˝

1˝

7/8˝

7/8˝

M24

M24

M24

M24

M30

M30

M30

M30

1 1/8˝

1˝

1˝


K5A

K8

K10

K11

K12

B1

B2

B3

C1

C2

D1

D2

89

90

91

92

93

94

95

96

97

98

99

100

K1B

85

K7

CF8-S14 × 158

84

K4

CF8-S14 × 145

83

88

CF6-S12 × 79

82

87

CF5-S12 × 96

81

K9

CF5-S10 × 68

86

CF4-S12 × 87

80

CF3-S12 × 65

CF8-U14 × 159

Test id.

79

Y. L. Yee (1984)

A. Mazroi (1984) (Continued)

77

78

Author

No.


410UB59.7

410UB59.7

310UB40.4

310UB40.4

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

W24 × 162

W24 × 162

W27 × 114

W27 × 114

W27 × 114

W24 × 100

W24 × 100

W24 × 162

Beam

460UB67.1

460UB67.1

310UB40.4

310UB40.4

310UC96.8

310UC96.8

310UC96.8

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

460UB67.1

W14 × 158

W14 × 145

W12 × 79

W12 × 96

W10 × 68

W12 × 87

W12 × 65

W14 × 159

Column

19.96

19.96

15.51

15.51

22.60

22.60

22.60

22.60

22.60

22.60

22.60

22.60

22.60

22.60

22.60

22.60

29.25

29.25

31.25

30.25

30.25

26.75

26.75

29.25

lp (in)

0.630

0.630

0.394

0.787

0.630

0.787

0.787

0.787

0.787

0.787

0.787

0.787

0.787

0.787

0.787

1.260

1.750

1.750

1.250

1.000

1.000

1.000

0.750

1.750

tp (in)

4.72

4.72

3.94

3.94

5.12

5.12

5.12

5.12

5.12

5.12

5.12

5.12

5.12

5.12

5.12

5.12

6.50

6.50

6.50

5.50

5.50

5.50

5.50

6.50

g (in)

4.44

4.44

3.94

3.94

5.22

5.22

5.22

5.22

5.22

5.22

5.22

5.22

5.22

5.22

5.22

5.22

5.47

5.47

4.93

3.93

3.93

3.50

3.50

5.47

pt (in)

M20

M20

M16

M20

M24

M24

M24

M24

M24

M24

M30

M24

M30

M30

M30

M30

1 1/8˝

1 1/8˝

1˝

1˝

1˝

7/8˝

7/8˝

1 1/8˝

db


R. Zandonini and P. Zanon (1988)

104

EP 1-5

EPB 1-2

EPB 1-3

EPB 1-4

EPB 1-5

CT1A-1

108

109

110

111

112

113

CT1A-3

CT1A-4

CT1A-5

CT1A-6

CT1B-1

CT1B-2

CT1B-3

CT1B-4

CT1B-5

CT1B-6

CT2A-1

CT2A-2

115

116

117

118

119

120

121

122

123

124

125

126

CT1A-2

EP 1-4

107

114

EP 1-3

EP 1-2

EP 1-1

J4

J3

JT/13B

106

105

L. F. L. Ribeiro et al. (1998)

D. B. Moore and P. A. C.Sims (1986)

102

103


101

VS350 × 58

VS350 × 58

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

VS250 × 37

IPE 300

IPE 300

IPE 300

IPE 300

IPE 300

IPE 300

IPE 300

IPE 300

IPE 300

UB 254 × 102 × 22

UB 254 × 102 × 22

UB 254 × 102 × 22

CVS350 × 128

CVS350 × 128

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

CVS350 × 105

—

—

—

—

—

—

—

—

—

UC 152 × 152 × 23

UC 152 × 152 × 23

UC 152 × 152 × 23

13.15

13.15

9.35

9.35

9.35

9.35

9.35

9.35

9.35

9.35

9.35

9.35

9.35

9.35

16.54

16.54

16.54

16.54

11.81

11.81

11.81

11.81

11.81

9.252

9.252

10.24

1.250

1.500

0.750

0.875

0.875

1.000

1.000

1.250

0.750

0.875

0.875

1.000

1.000

1.250

0.984

0.866

0.709

0.591

0.984

0.866

0.709

0.591

0.472

3.50

3.50

3.00

3.00

3.00

3.00

3.00

2.50

3.00

2.50

2.50

2.50

2.50

2.50

4.13

4.13

4.13

4.13

4.13

4.13

4.13

4.13

4.13

3.43

3.43

0.591 0.591

2.99

0.591

4.13

4.13

3.49

3.49

3.49

3.49

3.49

3.00

3.49

3.00

3.00

3.00

3.00

3.00

4.72

4.72

4.72

4.72

4.72

4.72

4.72

4.72

4.72

3.94

3.94

3.94

(Continues)

7/8˝

7/8˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

5/8˝

3/4˝

5/8˝

5/8˝

5/8˝

5/8˝

5/8˝

M20

M20

M20

M20

M20

M20

M20

M20

M20

M16

M16

M16


CT2B-2

CT2B-3

CT2B-4

CT2B-5

CT2B-6

7

132

133

134

135

136

137

14

15

16

17

18

FS1a

141

142

143

144

145

146

FS2a

FS2b

FS3a

148

149

150

FS1b

13

140

147

12

139

Ana M. Girao Coelho et al. (2004)

CT2B-1

131

11

CT2A-6

130

138

CT2A-5

CT2A-4

CT2A-3

Test id.

129


L. F. L. Ribeiro et al. (1998) (Continued)

127

128

Author

No.


IPE300

IPE300

IPE300

IPE300

IPE300

686 × 254 UB 125

457 × 191 UB 74

457 × 191 UB 74

762 × 267 UB 147

457 × 191 UB 74

762 × 267 UB 147

457 × 191 UB 74

457 × 191 UB 74

457 × 191 UB 74

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

VS350 × 58

Beam

HE340M

HE340M

HE340M

HE340M

HE340M

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 132

254 × 254 UC 132

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 73

254 × 254 UC 89

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

CVS350 × 128

Column

11.61

11.61

11.61

11.61

11.61

29.84

21.14

23.22

32.83

21.14

32.83

21.14

21.14

21.14

13.15

13.15

13.15

13.15

13.15

13.15

13.15

13.15

13.15

13.15

lp (in)

0.788

0.591

0.591

0.409

0.409

0.787

0.591

0.591

0.591

0.591

0.591

0.591

0.591

0.787

0.875

1.000

1.000

1.250

1.250

1.500

0.875

1.000

1.000

1.250

tp (in)

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

4.00

4.00

3.50

3.50

3.50

3.50

4.00

4.00

3.50

3.50

g (in)

3.54

3.54

3.54

3.54

3.54

3.94

3.94

3.94

3.94

3.94

3.94

3.94

3.94

3.94

4.63

4.63

4.13

4.13

4.13

4.13

4.63

4.63

4.13

4.13

pt (in)

M20

M20

M20

M20

M20

M24

M20

M24

M24

M24

M24

M24

M24

M24

1˝

1˝

7/8˝

7/8˝

7/8˝

7/8˝

1˝

1˝

7/8˝

7/8˝

db


FS4b

EEP_15_2

EEP_10_2a

EEP_10_2b

A-M



L. R. O. Lima (2003)

153

154

155

156

157

159

160

EE2

EE3

EE4

EE5

EE6

EE7

161

162

163

164

165

166

EE1

JD3

B-M

FS4a

152

158

FS3b

151

IPE240

IPE240

IPE240

IPE240

IPE240

IPE240

IPE240

H300 × 200 × 8 × 12

IPE330

IPE330

HE320A

HE320A

HE320A

IPE300

IPE300

IPE300

HEB240

HEB240

HEB240

HEB240

HEB240

HEB240

HEB240

H300 × 250 × 8 × 12

HEB160

HEB160

HE300M

HE300M

HE300M

HE340M

HE340M

HE340M

9.055

9.055

9.055

9.055

9.055

9.055

9.055

15.75

12.60

12.60

11.61

11.61

11.61

11.61

11.61

11.61

0.591

0.591

0.591

0.591

0.591

0.591

0.591

0.787

0.398

0.652

0.398

0.398

0.576

0.396

0.396

0.788

3.78

3.78

3.78

3.78

3.78

3.78

3.78

4.25

3.94

3.94

5.91

5.91

5.91

3.54

3.54

3.54

2.91

2.91

2.91

2.91

2.91

2.91

2.91

4.41

3.54

3.54

5.32

5.32

5.32

3.54

3.54

3.54

M20

M20

M20

M20

M20

M20

M20

M20

M20

M20

M24

M24

M24

M20

M20

M20


122


column gt ct nt

pt beam tp

pit pi pi

lp

li

ni

pic nc

pc cc

a

column gt ct nt

pt beam tp

li

pc

lp

ni

nc

cc gc b FIGURE 5.7 Size parameters for extended end-plate connection: (a) extended only on tension side; (b) extended on both tension and compression sides.


123

gc2 Distance from the outer line to the inner line of compression-side fasteners where the number of fastener lines exceeds three lp Plate length tp Plate thickness nt Total number of tension-side fasteners ni Total number of central fasteners nc Total number of compression-side fasteners The case of end-plate connections extended only on the tension side: pc Distance from the inner row of fasteners on the compression side to the center of the compression-side flange of the beam cc Distance from the center of the compression side flange of the beam to the compressionside edge of the plate The case of end-plate connections extended on both the tension and the compression sides: pc Distance between two rows of compression-side fasteners cc Distance from the outer row of fasteners on the compression side to the compressionside edge of the plate

5.2.6 Flush End-plate Connections

Originally, 24 experimental data conducted by Ostrander (1970) were installed in the database. Then, 15 experimental data conducted in the 1980s were appended. A total of 58 experimental data have been compiled in this database. Collected experimental moment-rotation data for flush end-plate connections are tabulated in Table 5.10. The notations for major parameters of this connection type as shown in Figure 5.8 are identified as follows: ct pt li pc cc pit pi pic gt gt2 g i gi2 gc gc2

Distance from the tension-side edge of plate to the outer surface of the tension-side flange of the beam Distance from the outer surface of the tension-side flange to the row of tension-side fasteners Distance from the center of tension-side fastener holes to the center of the compressionside fastener holes Distance from the row of compression-side fasteners to the outer surface of the compression-side flange of the beam Distance from the outer surface of the compression-side flange of the beam to the compression-side edge of the plate Distance from the row of tension-side fasteners to the upper row of central fasteners Distance between two inner rows of central fasteners Distance from the row of compression-side fasteners to the row of central fasteners Distance between two inner lines of tension-side fasteners Distance from the outer line to the inner line of the tension-side fasteners where the number of fastener lines exceeds three Distance between two inner lines of central fasteners Distance from the outer line to the inner line of the central fasteners where the number of fastener lines exceeds three Distance between two inner lines of the compression-side fasteners Distance from the outer line to the inner line of the compression-side fasteners where the number of fastener lines exceeds three

W12 × 27 W12 × 27

TEST 9 TEST 11 TEST 12 TEST 13 TEST 17 TEST 18 TEST 19 TEST 23 TEST 2 TEST 5 TEST 6 TEST 7 TEST 8 TEST 10 TEST 14 TEST 15 TEST 16 TEST 20 TEST 21 TEST 22 TEST 24

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

W12 × 27

W12 × 27

W12 × 27

W12 × 27

W12 × 27

W12 × 27

W12 × 27

W10 × 21

W10 × 21

W10 × 21

W10 × 21

W10 × 21

W10 × 21

W12 × 27

W12 × 27

W12 × 27

W12 × 27

W12 × 27

W10 × 21

W10 × 21

TEST 4

4

W10 × 21

W10 × 21

3

TEST 1

Beam

TEST 3

J. R. Ostrander (1970)

1

Test id.

2

Author

No.

TABLE 5.10 Collected test data for flush end-plate connections

W8 × 48

W8 × 24

W8 × 24

W8 × 24

W8 × 40

W8 × 40

W8 × 40

W8 × 28

W8 × 28

W8 × 28

W8 × 28

W8 × 28

W8 × 28

W8 × 48

W8 × 24

W8 × 24

W8 × 24

W8 × 40

W8 × 40

W8 × 40

W8 × 28

W8 × 28

W8 × 28

W8 × 28

Column

7.000

7.000

7.000

7.000

7.000

7.000

7.000

5.000

5.000

5.000

5.000

5.000

5.000

7.000

7.000

7.000

7.000

7.000

7.000

7.000

5.000

5.000

5.000

5.000

li (in)

4.00

4.00

4.00

4.00

4.00

4.00

4.00

3.50

3.50

3.50

3.50

3.50

3.50

4.00

4.00

4.00

4.00

4.00

4.00

4.00

3.50

3.50

3.50

3.50

g (in)

0.625

0.625

0.500

0.375

0.625

0.500

0.375

0.750

0.250

0.250

0.375

0.500

0.500

0.625

0.625

0.500

0.375

0.625

0.500

0.375

0.750

0.250

0.375

0.500

tp (in)

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

3/4˝

db


8 9 10

40

41

42

F1EP_10_2 F2EP_10_2

50

F2EP_15_2

49

48

F1EP_15_2

47

A. M. G. Coelho and F. S. K. Bijlaard (2007)

J7-M

J5-M

46

45

J1-M

TEST1

6

39

A. W. Thomson and B. M. Broderick (2002)

5

38

N. D. Brown and D. Anderson (2001)

4

37

44

3

43

2

36

1

FPC/M

35


BM5

32


BM4

31

34

BM3

30

33

BM2

BM1

28

J. Phillips and J. A. Packer (1981)

JT/12

29

JT/11B

JT/11

27


26

25

HE320A

HE320A

HE320A

HE320A

254 × 146 UB 37

254 × 146 UB 37

254 × 146 UB 37

457 × 152 UB 52

406 × 178 UB 60

457 × 191 UB 74

406 × 178 UB 60

686 × 254 UB 125

457 × 191 UB 74

406 × 178 UB 60

457 × 191 UB 74

406 × 178 UB 60

406 × 178 UB 60

IPE300

W250 × 33

W250 × 33

W250 × 33

W250 × 33

W250 × 33

UB 254 × 102 × 22

UB 254 × 102 × 22

UB 254 × 102 × 22

HE300M

HE300M

HE300M

HE300M

203 × 203 UC 86

203 × 203 UC 52

203 × 203 UC 86

203 × 203 UC 52

254 × 254 UC 73

254 × 254 UC 89

254 × 254 UC 73

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 73

—

W200 × 100

W200 × 100

W200 × 100

W200 × 100

W200 × 100

UC 152 × 152 × 23

UC 152 × 152 × 23

UC 152 × 152 × 23

6.299

6.299

6.299

6.299

5.354

5.354

5.354

13.78

11.28

13.27

11.28

21.97

13.27

11.28

13.27

11.28

11.28

7.087

6.693

6.693

6.693

6.693

6.693

5.906

5.906

5.906

5.91

5.91

5.91

5.91

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

3.54

4.13

3.15

3.15

3.15

3.15

3.15

2.99

2.99

2.99

M24

M24

M24

M24

M20

M20

M20

M20

M24

M20

M20

M24

M24

M24

M20

M20

M20

M20

7/8˝

7/8˝

7/8˝

7/8˝

7/8˝

M16

M16

M16

(Continues)

0.404

0.400

0.576

0.581

0.472

0.472

0.394

0.591

0.591

0.472

0.472

0.591

0.591

0.591

0.472

0.472

0.472

0.472

1.000

0.875

0.750

0.625

0.375

0.472

0.472

0.472


19 31 34 37 JD1

54

55

56

57

58


18

53

16 17

P. Zoetemeijer (1981)

51

Test id.

52

Author

No.


H300 × 200 × 8 × 12

IPE400

IPE400

IPE400

HE300A

HE300A

HE300A

HE300A

Beam

H300 × 250 × 8 × 12

—

—

—

—

—

—

—

Column

4.12

3.87

3.87

4.93

4.93

4.93

4.93

g (in)

6.929 4.25

11.47

11.72

11.72

5.937

5.937

7.591

7.591

li (in)

0.787

1.260

0.630

0.472

0.630

0.472

0.630

0.472

tp (in)

M20

M24

M24

M24

M24

M24

M24

M24

db



127

column gt ct pt

nt

beam tp

li

lp

pc cc

ni

nc

gc

FIGURE 5.8 Size parameters for flush end-plate connection.

lp tp nt ni nc

Plate length Plate thickness Total number of tension-side fasteners Total number of central fasteners Total number of compression-side fasteners

5.2.7 Header Plate Connections

Moment-rotation tests on header plate connections were firstly performed by Sommer at the University of Toronto in 1969. He conducted experiments on 20 specimens. In the 1980s, two series of experimental investigations were conducted by Davison et al. (1987) and Aggarwal (1990). A total of 26 experimental moment-rotation data has been installed as listed in Table 5.11. The notations for the major parameters of this connection type as shown in Figure 5.9 are identified as follows: lt ct p cc lc g lp tp tbw n

Distance from the tension-beam flange to the top edge of the plate Distance from the center of the upper fastener holes to the top edge of the plate Distance between two rows of fasteners Distance from the center of the lower fastener holes to the bottom edge of the plate Distance from the compression-beam flange to the bottom edge of the plate Distance between two lines of fasteners Plate depth Plate thickness Beam-web thickness Total number of fasteners

Test Id. TEST 5 TEST 6 TEST 7 TEST 8 TEST 9 TEST 10 TEST 11 TEST 12 TEST 13 TEST 14 TEST 15 TEST 16 TEST 17 TEST 18 TEST 19 TEST 20 TEST 25 TEST 26 TEST 27 TEST 28 JT/14 M2 M3 M4 M5 M6

Author

W. H. Sommer (1969)


A. K. Aggarwal (1990)

No.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

21

22 23 24 25 26

M16 M20 M20 M20 M24 M16

0.472 0.630 0.472 0.472 0.630 0.630

2.99 3.94 3.94 3.94 3.94 3.94

10.43 5.906 5.906 5.906 5.906 5.906 UC 203 × 203 × 46 UC 203 × 203 × 46 UC 203 × 203 × 46 UC 203 × 203 × 46 UC 203 × 203 × 46

UB 203 × 133 × 25 UB 203 × 133 × 25 UB 203 × 133 × 25 UB 203 × 133 × 25 UB 203 × 133 × 25

3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 3/4˝ 0.250 0.250 0.250 0.250 0.250 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.250 0.250 0.500 0.500 0.250 0.250 0.250 0.250 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 4.00 5.50 5.50 5.50 5.50 5.50 5.50 4.00 4.00 4.00 4.00 15.000 9.000 12.000 15.000 18.000 9.000 12.000 15.000 9.000 12.000 15.000 18.000 18.000 15.000 12.000 15.000 12.000 9.000 9.000 6.000 UC 152 × 152 × 23

— — — — — — — — — — — — — — — — — — — —

W18 × 45 W24 × 76 W24 × 76 W24 × 76 W24 × 76 W18 × 45 W18 × 45 W18 × 45 W24 × 76 W24 × 76 W24 × 76 W24 × 76 W24 × 76 W24 × 76 W24 × 76 W24 × 76 W18 × 45 W18 × 45 W12 × 27 W12 × 27

db

tp (in)

g (in)

lp (in)

UB 254 × 102 × 22

Column

Beam

TABLE 5.11 Collected test data for header-plate connections



129

column

g beam

lt ct p

tp

p cc tbw

lp

n

lc

FIGURE 5.9 Size parameters for header-plate connection.

5.3 Steel Connection Databank Program 5.3.1 Outline of SCDB

The experimental connection test data collected in the previous section can be controlled by the Steel Connection Data Bank (SCDB) program. The first version of the SCDB program has seven main routines. For use with any workstation or PC with a FORTRAN compiler, the plotter routines in it have been removed. In this book, general views of M–θr curves of experimental test data for each connection type are shown in the Appendix. The user can then verify his own plotter routine by comparing it with these figures. The latest version of SCDB program for this book consists of the following main routines:

1. Transform output unit system from original U.S. units to MKS units or SI units. 2. Set and print the selected test data. 3. Set and print general tables of test data concerning connection type and mode. 4. Determine and print the connection moment and tangent connection stiffness obtained from the three prediction equations for the selected test data.

In this program, three prediction equations are available: Frye-Morris polynomial model; modified exponential model; and three-parameter power model. The prediction curves obtained from the three-parameter power model are limited to the angle types of connection and header plate connections. In the three-parameter power model, the initial connection stiffness Rki and the ultimate connection moment Mu are based on the values determined from the simple mechanics and mechanism formulated by Kishi and Chen (1990). The shape parameter n is determined

130


numerically by applying the least mean squares technique for the connection moments between the experimental data and the model. The validity of either the three-parameter power model or the modified experimental model for practical use was numerically discussed by Kishi and Chen et al. (1991, 1993) and Kishi and Hasan et al. (1995). It was concluded that the three-parameter power model can replace the experimental data in adequately describing the connection M–θr behavior for practical use. Depending on the user’s requirements, it is possible to execute the SCDB program together with the above-mentioned routines. This program enables the user to make comparative studies of the role of different connection parameters on M–θr behavior.

5.3.2 User Manual for SCDB Program

The SCDB program is written in FORTRAN77, which is composed of four files (scdb1.f-scdb4.f ). These four files are provided in the source list of the J. Ross Web site (http://www.jrosspub.com/ wav/). The user can compile the files and then create the executable file, for which a hard disk is generally required. To execute the SCDB program, the files shown in Table 5.12 must be prepared. It should be noted that scdb.d and BANK/no1-BANK/no7 are files for input, while bank.d is for output. The files of BANK/no1-BANK/no7 are the files for the original database of each connection type and are provided on the J. Ross Web site. The file scdb.d should be defined in the same directory with an executable program, and input data should be created according to the user’s purpose as follows: Lines 1 to 7 (7a50) File names with full pass of files BANK/no1 to BANK/no7 Line 8 (4i5) idsi: 0: 1: 2: icnct: ilist: 0: n:

Index for unit name of output data Customary U.S. units MKS units except dimensions (cm) of connection SI units except dimensions (cm) of connection Identification number of the connection type referred to in Table 5.1 Flag for output Print the databank list Print the table concerning the nth fastening mode referred to in Table 5.13. Numbers 9 through 12 or numbers 16 and 17 are for the types of end-plate connections. nterm: Number of terms considered in the modified exponential curve-fitting equation. The case of nterm = 6 will give a good result. 0:

By default, 6 is set

Line 9 (i5) ngroup: Number of calculating group of experimental data for the type of connection given by icnct in Line 8 Line 10 (10i5) istart (i), i = 1, ngroup: Starting the sequential number of the experimental data in the ith group specified by the above variable ngroup


131

TABLE 5.12 List of files used in SCDB program File name

Contents

scdb.d

input file

BANK/no1-BANK/no7

Original data base of each connection type

bank.d

Output file

temp1, temp2

Working file

TABLE 5.13 Fastening mode patterns for making tables Pattern number

Fastening mode pattern

1

All riveted

2

All bolted

3

Riveted-to-beam and bolted-to-column

4

Bolted-to-beam and riveted-to-column

5

Riveted-to-beam and welded-to-column

6

Bolted-to-beam and welded-to-column

7

Welded-to-beam and riveted-to-column

8

Welded-to-beam and bolted-to-column

9

All riveted without column stiffener

10

All riveted with column stiffener

11


12

All bolted with column stiffener

13

Riveted/bolted-to-beam and column (1, 2, 3, 4)

14

Riveted/bolted-to-beam and welded-to-column (5, 6)

15

Riveted/bolted-to-column and welded-to-beam (7, 8)

16

Riveted/bolted without column stiffener (9, 11)

17

Riveted/bolted with column stiffener (10, 12)

20

All modes included

Line 11 (10i5) iend (i), i = 1, ngroup: Finishing the sequential number of experimental data in the ith group specified by the above variable ngroup

5.3.3 Examples

Example 1: Printing a database list The first example is for making a database list: connection parameters, experimental M–θr data, parameters for each prediction equation, and the comparison of the values obtained from experimental test data with the values from the prediction equations. The input file named scdb.d for this example is given in Table 5.14 and may be used for making a database list of the experimental

132


TABLE 5.14 Content of scdb.d for Example 1 BANK/no1 BANK/no2 BANK/no3 BANK/no4 BANK/no5 BANK/no6 BANK/no7 2 3 0 0 1 18 18

data of the sequential number 18 for the type of top- and seat-angle connection with double-web angle. The content of the output file bank.d is shown in Table 5.15 and can be used to verify the SCDB program upon installation on a computer system. Input and output files for this example are prepared in files of scdb_ex1.d and bank_ex1.d, respectively. Example 2: Printing the general tables of test data The second example is for making the general table of experimental data concerning connection type and mode. In this example, an attempt is made to produce a general table of experimental data concerning extended end-plate connection without column stiffener. The input file scdb.d for this example is given in Table 5.16. The output file bank.d obtained from the program SCDB is shown in Table 5.17. These files are provided in the files of scdb_ex2.d and bank_ex2.d, respectively.

5.4 Web Site of Connections The latest information of the semi-rigid connection database is available on http://struct .ce.muroran-it.ac.jp/. This Web page also includes the list of journals, textbooks, monographs, and some useful programs that are related to the steel semi-rigid connection or frame structures. We invite readers who have other experimental results of the semi-rigid connections to contact Dr. Masato Komuro about including their results.


133

TABLE 5.15 Content of bank.d for Example 1 III - 18 Connection type : Top-and seat-angle connections with double web angle Mode : All bolted Tested by : A.Azizinamini et al. (1985) U.S.A. Test id. : 14S9 Column : W12 × 96 Fasteners : A325- -M22.2D Beam : W14 × 38 M23.8 Oversize holes Material : A36 F.Angle : 6 × 4.0 × 1/2 × 8.0 W.Angle : 4 × 3.5 × 1/4 × 8.5 Fy = 272 MPa Fu = 468 MPa Major parameters ( cm ) lp = 21.5900 lu = 7.1437 ll = 7.1437 ta = 0.6350 gb = 5.0800 gc = 6.5888 cu = 3.1750 cl = 3.1750 pb = 7.6200 pc = 7.6200 nb = 1 × 3 nc = 1 × 3 It = 20.3200 tt = 1.2700 ts = 20.3200 ts = 1.2700 gt = 8.8900 gt´ = 6.3500 gs = 8.8900 gs´ = 6.3500 qt = 8.8900 rt = 13.9700 qs = 8.8900 rs = 13.9700 pt = 6.3500 ps = 6.3500 nt = 2 × 2 nt´ = 2 × 1 ns = 2 × 2 ns´ = 2 × 1 ) Heavy hex high strength bolts used Remark 1 2) No

Moment (kN-m)

Rotation (radians) × 1/1000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

0.00 4.28 8.55 11.94 15.32 21.20 27.26 31.90 36.53 40.36 44.19 47.85 51.50 55.52 59.53 62.92 66.31 70.95 75.59 79.61 83.63 87.75 91.87 96.89 99.95

0.00 0.15 0.31 0.42 0.52 0.77 1.08 1.30 1.51 1.70 1.89 2.13 2.38 2.66 2.94 3.24 3.54 4.07 4.60 5.20 5.79 6.75 7.70 9.12 10.56

No

Moment (kN-m)


26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44

102.12 104.29 105.74 107.19 108.73 110.27 111.28 112.29 112.49 112.69 113.52 114.34 115.98 116.62 117.27 118.36 119.45 120.54 121.63

11.71 12.86 13.88 14.90 15.96 17.01 18.18 19.34 20.27 21.20 22.21 23.21 24.35 25.29 26.24 27.05 27.87 28.78 29.70

(Continues)

( R : × 1/1000 radians )

C =

0.28596917E+00

RKj =

Bmo=

0.00000000E+00

59.53

66.31

75.59

0.31

0.52

1.08

1.51

1.89

2.38

2.94

3.54

4.60

5.79

3

5

7

9

11

13

15

17

19

21

83.63

51.50

44.19

36.53

27.26

15.32

8.55

0.00

0.00

1

Expri.


No

Nexp= 6

76.56

70.99

64.80

60.60

55.86

50.74

46.07

39.13

25.47

17.16

0.00

Poly.

83.52

75.76

66.08

59.20

51.53

43.58

36.84

27.96

14.61

8.83

0.00

M.Expo.

Moment ( kN−m )

82.60

75.82

67.82

62.18

55.76

48.85

42.70

34.07

19.60

12.51

0.00

P.Model.

0.5815E+01

0.7799E+01

0.1047E+02

0.1292E+02

0.1451E+02

0.1808E+02

0.2097E+02

0.2063E+02

0.2915E+02

0.2996E+02

0.2777E+02

Expri.

0.4245E+01

0.5195E+01

0.6550E+01

0.7705E+01

0.9292E+01

0.1144E+02

0.1388E+02

0.1861E+02

0.3305E+02

0.4519E+02

0.6277E+02

Poly.

0.5458E+01

0.7731E+01

0.1062E+02

0.1263E+02

0.1484E+02

0.1715E+02

0.1916E+02

0.2191E+02

0.2606E+02

0.2768E+02

0.2954E+02

M.Expo.

Connection stiffness ( kN−m ) × 1000

0.4976E+01

0.6529E+01

0.8678E+01

0.1041E+02

0.1261E+02

0.1528E+02

0.1793E+02

0.2212E+02

0.3060E+02

0.3560E+02

0.4721E+02

P.Model.

0.26430784E+03 −0.17687217E+04 0.47893731E+04 −0.55406128E+04 0.23828771E+04

Power model : Bm = ( Rki × R ) / ( 1 + ( R/R0 )**rn )**( 1/rn ) rn = 0.880 rki = 0.47207127E+02 rmu = 0.13448064E+03

23.2100

0.10143474E+01

Rj0 =

AI = −0.12052011E+02

0

Nliner= 1

Q3 =

Bm = Sum ( Ai × ( 1 − exp( − R/( 2*i*C ) ) ) ) + Sum ( RKj × ( R − Rj0 ) ) + Bm0

Modified exponential model :

R = Sum ( Ai × ( K*Bm )**Pi × 10**Qi ) Frye and Morris polynomial model : t = 1.270000 d = 35.877500 tc = 0.635000 w = 20.320000 g = 5.238750 K = 0.010631 A1 = 1.498414 A2 = 5.596349 A3 = 4.344317 P1 = 1 P2 = 3 P3 = 5 Q1 = 0 Q2 = 0

Moment-rotation prediction equations

Table 5.15 (continued)


12.86

14.90

17.01

19.34

21.20

23.21

25.29

27.05

28.78

25

27

29

31

33

35

37

39

41

43

120.54

118.36

116.62

114.34

112.69

112.29

110.27

107.19

104.29

99.95

91.87

120.63

118.74

116.67

114.10

111.41

108.73

105.04

101.31

97.24

91.93

83.71

166

1

1

2 5 11 0

BANK/no7

BANK/no6

BANK/no5

BANK/no4

BANK/no3

BANK/no2

BANK/no1

TABLE 5.16 Content of scdb.d for Example 2

7.70

10.56

23

120.50

118.57

116.51

113.89

113.12

112.08

110.14

107.62

104.37

99.70

91.78

116.97

116.12

115.15

113.85

112.40

110.86

108.55

105.99

102.92

98.47

90.53

0.1196E+01

0.1332E+01

0.6857E+00

0.1113E+01

0.5073E+00

0.5056E+00

0.1179E+01

0.1440E+01

0.1639E+01

0.1989E+01

0.4000E+01

0.1070E+01

0.1128E+01

0.1195E+01

0.1285E+01

0.1387E+01

0.1500E+01

0.1673E+01

0.1873E+01

0.2126E+01

0.2518E+01

0.3309E+01

0.1097E+01

0.1140E+01

0.1205E+01

0.1318E+01

0.4657E+00

0.6709E+00

0.1011E+01

0.1388E+01

0.1792E+01

0.2293E+01

0.3443E+01

0.4695E+00

0.5203E+00

0.5813E+00

0.6686E+00

0.7741E+00

0.8961E+00

0.1096E+01

0.1344E+01

0.1679E+01

0.2236E+01

0.3455E+01


TEST A2-R

TEST A3-L

TEST A3-R

TEST C1

14

15

16

17

TEST C3

TEST C4

TEST C5

19

20

21

TEST C2

TEST A2-L

13

18

TEST A1-R

12


J. R. Bailey (1970)

11

TEST A1-L

TEST A1


10

TEST 1

7

TEST 3

TEST 6

6

TEST 2

TEST 5

5

9

TEST 4

8

TEST 3

4

TEST 2

TEST 1

Test id.

3

R. J. Dews (1979)


1

2

Author

No

1

TABLE 5.17 Content of bank.d for Example 2

15 × 6 UB 40

15 × 6 UB 40

15 × 6 UB 40

15 × 6 UB 40

12 × 5 UB 25

10 × 4 UB 19

10 × 4 UB 19

10 × 4 UB 17

10 × 4 UB 17

12 × 5 RSJ 32

12 × 5 RSJ 32

15 × 5 RSJ 42

W16 × 26

W14 × 22

W14 × 22

W24 × 55

W18 × 35

W14 × 22

W24 × 55

W18 × 35

W14 × 22

Beam

10 × 10 UC 60

10 × 10 UC 60

10 × 10 UC 60

10 × 10 UC 60

8 × 8 UC 48

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 40

8 × 8 UC 48

8 × 8 UC 48

8 × 8 UC 35

W10 × 33

W8 × 31

W8 × 31

W14 × 48

W10 × 49

W8 × 35

W14 × 48

W10 × 49

W8 × 35

Column

lp(cm)

36.8300

36.8300

36.8300

36.8300

29.2100

—

—

—

—

—

—

36.8300

49.4894

43.8556

43.5762

69.2150

54.6100

43.8150

69.2150

54.6100

43.8150


V. Extended end-plate connections

2.5400

2.5400

1.9050

1.9050

1.9050

2.1590

2.1590

2.0447

2.0447

2.5908

2.5908

3.1750

3.9675

2.3825

2.4613

3.1750

3.1750

2.2225

2.2225

1.9050

1.5875

tp(cm)

8.6900

8.8900

8.8900

8.8900

8.8900

—

—

—

—

—

—

10.1600

13.6525

14.0487

13.9700

13.9700

13.9700

13.9700

13.9700

13.9700

13.9700

g(cm)

11.4300

11.4300

11.4300

11.4300

11.4300

11.1125

11.1125

11.1125

11.1125

11.4300

M25.4

M25.4

M25.4

M19.1

M19.1

M19.1

M19.1

M15.9

M15.9

M22.2

M22.2

M19.1

8.8900 11.4300

M25.4

M19.1

M19.1

M25.4

M22.2

M19.1

M25.4

M22.2

M19.1

db

9.5250

8.8900

8.8900

10.1600

9.5250

8.8900

10.1600

9.5250

8.8900

pt(cm)


JT/13B

48


D2

47

B2

44

D1

CF8-U14 × 1

43

46

CF6-U14 × 1

42

B3

CF6-U12 × 9

41

Y. L. Yee (1984)

CF5-U10 × 4

40

45

CF5-U14 × 6

CF4-U12 × 8

35

CF5-U10 × 6

EP8 With shim

34

39

EP8

33

38

EP7 With shim

32

CF4-U12 × 1

EP7

31

CF4-U12 × 1

EP6

30

37

EP5

36

EP4

29

EP3

28

A. Mazroi (1984)

A. Mazroi (1983)

27

T2

T1

P. Grundy et al. (1980)

26

25

TEST J2

TEST J1

TEST J3


24

23

22

UB 254 × 102 × 22

410UB59.7

410UB59.7

460UB67.1

460UB67.1

W24 × 162

W27 × 114

W27 × 114

W27 × 114

W27 × 114

W27 × 114

W24 × 100

W24 × 100

W24 × 100

W24 × 162

W24 × 162

W24 × 162

W24 × 162

W27 × 114

W27 × 114

W24 × 100

W24 × 100

610 UB 113

610 UB 113

254 × 102 UB 2

254 × 102 UB 2

254 × 102 UB 2

UC 152 × 152 × 23

460UB867.1

460UB67.1

310UC96.8

310UC96.8

W14 × 159

W14 × 158

W12 × 96

W10 × 49

W14 × 61

W10 × 68

W12 × 120

W12 × 106

W12 × 87

—

—

—

—

—

—

—

—

310 UC 240

310 UC 240

152 × 152 UC 2

152 × 152 UC 3

152 × 152 UC 3

25.9999

50.6997

50.6997

57.3999

57.3999

74.2950

79.3750

79.3750

76.8353

76.8353

76.8353

67.9450

67.9450

67.9450

74.2950

74.2950

71.7550

71.7550

79.3750

76.8353

67.9450

67.9450

65.4924

65.4924

24.8001

24.8001

24.8001

1.5001

1.5999

1.5999

1.5999

2.0000

4.4450

3.1750

3.1750

2.5400

2.5400

2.5400

2.5400

2.5400

2.5400

4.4450

4.4450

3.8100

3.8100

3.1750

2.5400

2.5400

1.9050

3.1750

2.5400

1.5001

1.5001

1.5001

7.5999

12.0000

12.0000

13.0000

13.0000

16.5100

16.5100

16.5100

13.9700

13.9700

13.9700

13.9700

13.9700

13.9700

16.5100

16.5100

13.9700

13.9700

16.5100

13.9700

13.9700

13.9700

8.8900

8.8900

8.5999

8.5999

8.5999

M16

M20

M20

M24

M24

M28.6

M25.4

M25.4

M25.4

M25.4

M25.4

M22.2

M22.2

M22.2

M28.6

M28.6

M28.6

M28.6

M25.4

M25.4

M22.2

M22.2

M22.2

M22.2

M16

M16

M16

(Continues)

10.0000

11.2799

11.2799

13.2700

13.2700

13.8938

12.5222

12.5222

9.9822

9.9822

9.9822

8.8900

8.8900

8.8900

13.8938

13.8938

11.3538

11.3538

12.5222

9.9822

8.8900

8.8900

9.5250

9.5250

9.7000

9.7000

9.7000



51

14

15

16

17

18

FS1a

55

56

57

58

59

60

FS3b

FS4a

FS4b

EEP_15_2

EEP_10_2a

EEP_10_2b

A–M

65

66

67

68

69

70

71

B–M

FS3a

64

72

FS2b

FS2a

63

62


13

54

FS1b

12

61

11

53

7

J4

J3

Test id.

52

Ana M. Girao Coelho et al. (2004, 2007)

D. B. Moore and P. A. C. Sims (1986)

49

50

Author

No


IPE330

IPE330

HE320A

HE320A

HE320A

IPE300

IPE300

IPE300

IPE300

IPE300

IPE300

IPE300

IPE300

686 × 254 UB 125

457 × 191 UB 74

457 × 191 UB 74

762 × 267 UB 147

457 × 191 UB 74

762 × 267 UB 147

457 × 191 UB 74

457 × 191 UB 74

457 × 191 UB 74

UB 254 × 102 × 22

UB 254 × 102 × 22

Beam

HEB160

HEB160

HE300M

HE300M

HE300M

HE340M

HE340M

HE340M

HE340M

HE340M

HE340M

HE340M

HE340M

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 132

254 × 254 UC 132

254 × 254 UC 89

254 × 254 UC 89

254 × 254 UC 73

254 × 254 UC 89

UC 152 × 152 × 23

UC 152 × 152 × 23

Column

32.0000

32.0000

29.5001

29.5001

29.5001

29.5000

29.5000

29.5000

29.5000

29.5000

29.5000

29.5000

29.5000

75.7900

53.7000

58.9751

83.3999

53.7000

83.3999

53.7000

53.7000

53.7000

23.4998

23.4998

lp(cm)

1.0100

1.6550

1.0100

1.0100

1.4620

1.0060

1.0060

2.0020

2.0020

1.5010

1.5010

1.0399

1.0399

2.0000

1.5001

1.5001

1.5001

1.5001

1.5001

1.5001

1.5001

2.0000

1.5001

1.5001

tp(cm)

10.0000

10.0000

15.0000

15.0000

15.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

8.7000

8.7000

g(cm)

9.0000

9.0000

13.5001

13.5001

13.5001

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

9.0000

10.0000

10.0000

10.0000

10.0000

10.0000

10.0000

10.0000

10.0000

10.0000

10.0000

10.0000

pt(cm)

M20

M20

M24

M24

M24

M20

M20

M20

M20

M20

M20

M20

M20

M24

M20

M24

M24

M24

M24

M24

M24

M24

M16

M16

db


EE3

EE4

EE5

EE6

EE7

75

76

77

78

79

EE1

EE2

L. R. O. Lima (2003)

74

73

IPE240

IPE240

IPE240

IPE240

IPE240

IPE240

IPE240

HEB240

HEB240

HEB240

HEB240

HEB240

HEB240

HEB240

23.0000

23.0000

23.0000

23.0000

23.0000

23.0000

23.0000

1.5000

1.5000

1.5000

1.5000

1.5000

1.5000

1.5000

9.6000

9.6000

9.6000

9.6000

9.6000

9.6000

9.6000

7.4000

7.4000

7.4000

7.4000

7.4000

7.4000

7.4000

M20

M20

M20

M20

M20

M20

M20


140


References Aggarwal, A. K., Behaviour of flexible end-plate beam-to-column joints, Journal of Constructional Steel Research, 16(2), 111–134, 1990. AISC, Load and Resistance Factor Design Specifications for Structural Steel Buildings, 2nd edition, American Institute of Steel Construction, Chicago, IL, 1994. AISC, Allowable Stress Design and Plastic Design Specifications for Structural Steel Buildings, 9th edition, American Institute of Steel Construction, Chicago, IL, 1989. Altman, W. G., Jr., Azizinamini, A., Bradburn, J. H., and Radziminski, J. B., Moment-rotation characteristics of semi-rigid steel beam-to-column connection, Department of Civil Engineering, University of South Carolina, Columbia, SC, 1982. Azizinamini, A., Bradburn, J. H., and Radziminski, J. B., Static and cyclic behavior of semi-rigid steel beamcolumn connections, Department of Civil Engineering, University of South Carolina, Columbia, SC, 1985. Bailey, J. R., Strength and rigidity of bolted beam-to-column connections, Proceedings of the Conference on Joints in Structures, University of Sheffield, Sheffield, England, 1(4), 1970. Bell, W. G., Chesson, E. Jr., and Munse, W. H., Static tests of standard riveted and bolted beam-to-column connections, University of Illinois Engineering Experiment Station, Urbana, IL, 1958. Bernuzzi, C., Zandonini, R., and Zanon, P., Experimental analysis and modeling of semi-rigid steel joints under cyclic reversal loading, Journal of Constructional Steel Research, 38(2), 95–123, 1996. Bose, B., Youngson, G. K., and Wang, Z. M., An appraisal of the design rules in Eurocode 3 for bolted endplate joints by comparison with experimental results, Proceedings of the Institution of Civil Engineers, Structures and Buildings, 116(2), 221–234, 1996. Bose, B., Moment-rotation characteristics of semi-rigid joints in steel structures, Journal of the Institution of Engineers (India), Part CI, Civil Engineering Division, 62(2), 128–132, 1981. Brown, N. D. and Anderson, D., Structural properties of composite major axis end plate connections, Journal of Constructional Steel Research, 57(3), 327–349, 2001. Cabrero, J. M. and Bayo, E., The semi-rigid behaviour of three-dimensional steel beam-to-column joints subjected to proportional loading. Part I. Experimental evaluation, Journal of Constructional Steel Research, 63(9), 1241–1253, 2007. Calado, L., De Matteis, G., and Landolfo, R., Experimental response of top and seat angle semi-rigid steel frame connections, Materials and Structures, 33(8), 499–510, 2000. Chen, W. F. and Kishi, N., Semirigid steel beam-to-column connections: Data base and modeling, Journal of Structural Engineering, ASCE, 115(1), 105–119, 1989. Davison, J. B., Kirby, P. A., and Nethercot, D. A., Rotational stiffness characteristics of steel beam-to-column connections, Journal of Constructional Steel Research, 8, 17–54, 1987. Dews, R. J., Experimental test results on experimental end-plate moment connections, Thesis presented to Vanderbilt University, in partial fulfillment of the requirements for the degree of Master of Science, Nashville, TN, 1979. Elnashai, A. S., Elghazouli, A. Y., and Denesh-Ashtiani, F. A., Response of semirigid steel frames to cyclic and earthquake loads, Journal of Structural Engineering, ASCE, 124(8), 857–867, 1998. Fu, Z., Ohi, K., Takanashi, K., and Lin, X., Seismic behavior of steel frames with semi-rigid connections and braces, Journal of Constructional Steel Research, 46(1), 440–441(2), 1998. Gang, S., Yongjiu, S., and Yuanqing, W., Behaviour of end-plate moment connections under earthquake loading, Engineering Structures, 29(5), 703–716, 2007. Girão Coelho, A. M. and Bijlaard, F. S. K., Experimental behaviour of high strength steel end-plate connections, Journal of Constructional Steel Research, 63(9), 1228–1240, 2007. Girão Coelho, A. M., Bijlaard, F. S. K., and Simões da Silva, L., Experimental assessment of the ductility of extended end plate connections, Engineering Structures, 26(9), 1185–1206, 2004. Goverdhan, A. V., A collection of experimental moment-rotation curves and evaluation of prediction equations for semi-rigid connections, Thesis presented to Vanderbilt University, in partial fulfillment of the requirements for the degree of Master of Science, Nashville, TN, 1983.


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Grundy, P., Thomas, I. R., and Bennetts, I. D., Beam-to-column moment connections, Journal of the Structural Division, ASCE, 106(1), 313–330, 1980. Harper, W. L., Jr., Dynamic response of steel frames with semi-rigid connections, Structural research studies, Department of Civil Engineering, University of South Carolina, Columbia, SC, 1990. Hechtman, R. A. and Johnston, B. G., Riveted semi-rigid beam-to-column building connections, Progress Report No. 1, AISC Committee of Steel Structures Research, Lehigh University, Bethlehem, PA, 1947. Ioannides, S. A., Flange behavior in bolted end-plate moment connections, Thesis presented to Vanderbilt University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Nashville, TN, 1978. Johnson, L. G., Cannon, J. C., and Spooner, L. A., High tensile preloaded bolted joints for development of full plastic moments, British Welding Journal, 7, 560–569, 1960. Johnstone, N. D. and Waldpole, W. R., Bolted end-plate beam-to-column connections under earthquake type loading, Research Report 81(7), Department of Civil Engineering, University of Canterbury, Christchurch, New Zealand, 1981. Kishi, N., Hasan, R., Chen, W. F., and Goto, Y., Power model for semi-rigid connections, Steel Structures, Journal of Singapore Structural Steel Society, 5(1), 37–48, 1995. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K. G., Design aid of semi-rigid connections for frame analysis, AISC Engineering Journal, 30(3), 90–107, 1993. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K. G., Applicability of three-parameter power model to structural analysis of flexibly jointed frames, Proceedings of Mechanics Computing in 1990’s and Beyond, H. Adeli and R. L. Sierakowski eds., Columbus, OH, May 20–22, 233–237, 1991. Kishi, N. and Chen, W. F., Moment-rotation relations of semi-rigid connections with angles, Journal of Structural Engineering, ASCE, 116(7), 1813–1834, 1990. Kishi, N. and Chen, W. F., Steel connection data bank program, Structural Engineering, CE-STR-86-18, School of Civil Engineering, Purdue University, West Lafayette, IN, 1986a. Kishi, N. and Chen, W. F., Data base of steel beam-to-column connections, Structural Engineering, CESTR-86-26, School of Civil Engineering, Purdue University, West Lafayette, IN, 1986b. Komuro, M. and Kishi, N., Update of bolted semi-rigid connection database, Summaries of Technical Papers of Annual Meeting, Architectural Institute of Japan, CD-ROM, 2009. (Japanese) Komuro, M., Kishi, N., and Matsuoka, K. G., Static loading tests for moment-rotation relation of top- and seat-angle connections, Journal of Constructional Steel, JSSC, 10, 57–64, 2002. (Japanese) Kubo, N., Yoshida, T., Hashimoto, K., and Tanuma, Y., Column influence on the moment-rotation behaviour of semi-rigid angle connections, Journal of Construction Steel, JSSC, 7, 427–434, 1999. (Japanese) Lewitt, C. W., Chesson, E., Jr., and Munse, W. H., Restraint characteristics of flexible riveted and bolted beamto-column connections, Department of Civil Engineering, University of Illinois, Urbana, IL, 1966. Lima, L. R. O. de, Behaviour of structural steel endplate joints subjected to bending moment and axial force, Ph. D. Thesis, Departamento de Engenharia Civil, Pontifícia Universidade Católica do Rio de Janeiro, 2003. (Portuguese) Lipson, S. L., Single angle welded-bolted connections, Journal of the Structural Division, ASCE, 103(3), 559– 571, 1977. Lipson, S. L., Single-angle and single-plate beam framing connections, Proceedings of Canadian Structural Engineering Conference, Toronto, Canada, 141-162, 1968. Mander, J. B., Chen, S. S., and Pekcan, G., Low-cycle fatigue behavior of semi-rigid top-and-seat angle connections, AISC Engineering Journal, 31(3), 111–122, 1994. Marley, M. J. and Gerstle, K. H., Analysis and tests of flexibly-connected steel frames, Report to AISC under Project 199, AISC, Chicago, IL, 1982. Maxwell, S. M., et al., A realistic approach to the performance and application of semi-rigid jointed structures, Joints in Structural Steelwork, J. H. Howlett, W. M. Jenkins, and R. Stainsby, eds., Pentech Press, United Kingdom, 2.71–2.98, 1981. Mazroi, A., Moment-rotation behavior of beam-to-column end-plate connections in multi-story frames, Thesis presented to the University of Oklahoma, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Norman, OK, 1990.

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Moore, D. B. and Sims P. A. C., Preliminary investigations into the behaviour of extended end-plate steel connections with backing plates, Journal of Constructional Steel Research, 6(2), 95–122, 1986. Nethercot, D. A., Steel beam-to-column connections-A review of test data, CIRIA Project 338, London, 1985. Ostrander, J. R., An experimental investigation of end-plate connections, Thesis presented to the University of Saskatchewan, in partial fulfillment of the requirements for the degree of Master of Science, Saskatchewan, Canada, 1970. Packer, J. A. and Morris, L. J., A limit state design method for the tension region of bolted beam-column connections, The Structural Engineering, 55(10), 446–458, 1977. Phillips, J. and Packer, J. A., The effect of plate thickness on flush end-plate connections, Joints in Structural Steelwork, J. H. Howlett, W. M. Jenkins, and R. Stainsby, eds., Pentech Press, UK, 6.77–6.92, 1981. Rathbun, J. C., Elastic properties of riveted connections, Transactions of ASCE, 101, 524–563, 1936. Ribeiro, L. F. L., Gonçalves R. M., and Castiglioni C. A., Beam-to-column end plate connections—An experimental analysis, Journal of Constructional Steel Research, 46(1), 264–266, 1998. Richard, R. M., Kriegh, J. D., and Hormby, D. E., Design of single plate framing connections with A307 bolts, AISC Engineering Journal, 19(4), 209–213, 1982. Roeder, C. W., Knechtel, B., Thomas, E., Vaneaton, A., Leon, R. T., and Preece, F. R., Seismic behavior of older steel structures, Journal of Structural Engineering, ASCE, 122(4), 365–373, 1996. Sato, Y., Komuro, M., and Kishi, N., Experimental study on moment-rotation of top- and seat-angle connections, Journal of Constructional Steel Research, JSSC, 15, 121–128, 2007. (Japanese) Sherbourne, A. N., Bolted beam-to-column connections, The Structural Engineering, 39(6), 203–210, 1961. Sommer, W. H., Behavior of welded-header-plate connections, Thesis presented to University of Toronto, in partial fulfillment of the requirements for the degree of Master of Applied Science, Toronto, Canada, 1969. Surtees, J. O. and Mann, A. P., End plate connection in plastically designed structures, Proceedings of the International Conference on Joints in Structures, 1(5), University of Sheffield, Sheffield, England, 1970. Thompson, L. E., McKee, R. J., and Visintainer, D. A., An investigation of rotation characteristic of web shear framed connections using A-36 and A-441 steels, Technical report, Department of Civil Engineering, University of Missouri, Rolla, MO, 1970. Thomson, A. W. and Broderick, B. M., Earthquake resistance of flush end-plate steel joints for moment frames, Proceedings of Institution of Civil Engineers, Structures and Buildings, 152(2), 157–165, 2002. Yang, J. G. and Lee, G. Y., Analytical models for the initial stiffness and ultimate moment of a double angle connection, Engineering Structures, 29(4), 542–551, 2007. Yee, Y. L., Prediction of nonlinear behaviour of end-plate eave connections, Thesis presented to Monash University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Department of Civil Engineering, Victoria, Australia, 1984. Zandonini, R. and Zanon, P., Experimental analysis of end plate connections, Connections in Steel Structures; Behavior, Strength and Design, R. Bjorhovde, J. Brozzetti, and A. Colson, eds., Elsevier Applied Science Publishers, London, England, 41–51, 1988. Zoetemeijer, P., Semi-rigid bolted beam-to-column connections with stiffened column flanges and flush-end plates, In Joints in Structural Steelwork, Pentech Press, London, 2.99–2.118, 1981.

6

Advanced Analysis of Steel and Composite Semi-rigid Frames

Hong Chen Offshore Technology Development Pte Ltd, Keppel Offshore & Marine, Singapore J. Y. Richard Liew Department of Civil Engineering, National University of Singapore, Singapore

6.1 Structural Frames.................................................................................................................. 143 Rigid Frames • Simple Frames • Bracing Systems • Braced Versus Unbraced Frames • Sway Versus Nonsway Frames • Joint Representation • Analysis and Design of Semirigid Frames • Frame Stability 6.2 Advanced Analysis of Steel Frames..................................................................................... 154 Development of Advanced Analysis • Stiffness Formulation of Beam-column • Modeling of Material Nonlinearity in Beam-column • Updating of Element Forces and Geometry in Beam-column • Modeling of Truss Element • Modeling of Semi-rigid Connections • Modeling of Tubular Joints • Tubular Frame with K-type Joints • Bowstring Column • Bowstring Frame • Fire Analysis of Semi-rigid Frame 6.3 Advanced Analysis of Composite Frames.......................................................................... 211 Composite Members—Advanced Analysis • Modeling of Composite Column • Modeling of Composite Beam • Modeling of Building Core Wall • Modeling of Composite Semi-rigid End-plate Connection • Analysis of 20-Story Steel Frame with Composite Beams • Analysis of Core-braced Multistory Frame Appendix 1 Elastic Stiffness Matrix, ke. ...................................................................................... 251 Appendix 2 Geometric Stiffness Matrix, kg................................................................................ 252 Appendix 3 Bowing Matrix, kb..................................................................................................... 253

6.1 Structural Frames A structural framing system generally refers to geometric arrangement of the frame elements such as beams, columns, braces (if any), and shear walls (or core). Connections are used as a means of joining together the framing elements. The structural framing system shall be capable of resisting the design loads including gravity and lateral loads. The building structure shall be a combination of braced frames, unbraced frames, and shear walls that are capable of resisting the design loads. The stability of a simple frame (an unbraced frame with simple connections) shall be provided by a lateral load resisting framing system. For more complicated three-dimensional (3-D) structures involving the interaction of different structural systems, simple models are use143

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ful for preliminary design and for checking computer results. These models should capture the behavior of individual subframes and their effects on the overall structures.

6.1.1 Rigid Frames

A rigid frame derives its lateral stiffness mainly from the bending rigidity of frame members interconnected by rigid joints. The joints shall be designed in such a manner that they have enough strength and stiffness and negligible deformation. The deformation must be small enough to have any significant influence on the distribution of internal forces and moments in the structure or on the overall frame deformation. An unbraced rigid frame should be capable of resisting lateral loads without relying on an additional bracing system for stability. By itself, the frame has to resist the design forces including gravity and lateral forces. At the same time, it should have adequate lateral stiffness against side sway when subjected to horizontal wind or earthquake loads. Even though the detailing of the rigid joints results in a less economic structure, rigid unbraced frame systems perform better in a load reversal situation or in earthquakes. From architectural and functional points of view, it can be advantageous not to have any triangulated bracing systems or shear wall systems in the building.

6.1.2 Simple Frames

A simple frame referred to a structural system in which the beams and columns are pinned connected and the system is incapable of resisting any lateral loads. The stability of the entire structure must be provided by attaching the simple frame to some forms of bracing systems. The lateral loads are resisted by the bracing systems while the gravity loads are resisted by both the simple frame and the bracing system. In most cases, the lateral load response of the bracing system is sufficiently small such that second-order effects may be neglected for the design of the frames. Thus, the simple frames that are attached to the bracing system may be classified as nonsway frames. Figure 6.1 shows the principal components—the simple frame and bracing system—of such a structure. There are several reasons for adopting pinned (or flexible) connections in the design of multistory steel frames:

1. Pin-jointed frames are easier to fabricate and erect. For steel structures, it is more convenient to join the webs of the members without connecting the flanges. 2. Bolted connections are preferred over welded connections, which normally require weld inspection, weather protection, and surface preparation. 3. It is easier to design and analyze a building structure that can be separated into systemresisting vertical loads and system-resisting horizontal loads. For example, if all the girders are simply supported between the columns, the sizing of the simply supported girders and the columns is a straightforward task. 4. It is more cost effective to reduce the horizontal drift by means of bracing systems added to the simple framing than it is to use unbraced frame systems with rigid connections.

Actual connections in structures do not always fall within the categories of pinned or rigid connections. Practical connections are semi-rigid in nature and therefore the pinned and rigid conditions are only idealizations. Modern design codes allow the design of semi-rigid frames using the concept of wind-moment design (type-2 connections). In wind-moment design, the connection is assumed to be capable of transmitting only part of the bending moments (those due to the wind


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Simple connections

Bracing frame

Simple frame

FIGURE 6.1 Simple braced frame.

only). Recent development in the analysis and design of semi-rigid steel and composite frames can be obtained from Chen et al (1996), Leon et al. (1996), and Leon (1998). Design guidance is also available in Section 6 and Annex J of Eurocode 3 (CEN, 1992).

6.1.3 Bracing Systems

Bracing systems provide lateral stability to the overall framework. It may be in the forms of triangulated frames, shear wall or cores, or rigid-jointed frames. It is common to find bracing systems represented as shown in Figure 6.2. In steel structures, it is common to have a triangulated vertical truss to provide bracing (see Figure 6.2a). Unlike concrete structures where all the joints are naturally continuous, the most direct way to make connections between steel members is to hinge one member to the other. For a stiff structure, shear wall or core wall is often used (Figure 6.2b). The efficiency of a building to resist lateral forces depends on the location and type of the bracing systems employed, and the presence or otherwise of shear walls and cores around lift shafts and stairwells.

6.1.4 Braced Versus Unbraced Frames

An unbraced frame comprises beams and columns without braces. Rigid connections shall be provided in an unbraced frame that is intended to carry lateral forces. A bracing frame resists lateral forces through the trussing action of diagonal braces or shear wall.

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a

b FIGURE 6.2 Common bracing systems: (a) vertical truss system; (b) shear wall system.

Figures 6.3 and 6.4 represent the structures that can be easily defined, within one system, two subassemblies identifying the bracing system and the system to be braced. For the structure shown in Figure 6.3, there is a clear separation of functions in which the gravity loads are resisted by the hinged subassembly (Frame B) and the horizontal loads are resisted by the braced assembly (Frame A). In contrast, for the frame in Figure 6.4, since Frame B is able to resist horizontal actions as well as vertical actions, it is necessary to assume that practically all the horizontal actions are resisted by Frame A in order to define this system as braced. According to Section 5.2 of Eurocode 3 (CEN, 1992) a frame may be classified as braced if its sway resistance is supplied by a bracing system in which its response to lateral loads is sufficiently


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=

+

Frame A

Frame B

FIGURE 6.3 Frames split into two subassemblies: Frame A-bracing system. Frame B-simple frame.

=

+

Frame A

Frame B

FIGURE 6.4 Mixed frames split into two subassemblies: Frame A-bracing frame, Frame B-unbraced frame.

stiff for it to be acceptably accurate to assume all horizontal loads are resisted by the bracing system. The frame can be classified as braced if the bracing system reduces its horizontal displacement by at least 80 percent. For the frame shown in Figure 6.3, the simple frame (Frame B) has no lateral stiffness, and the Truss frame (Frame A) resists all lateral load. In this case, Frame B is considered to be braced by Frame A. For the frame shown in Figure 6.4, Frame B may be considered a braced frame if the following deflection criterion is satisfied:  ∆A   1 − ∆  ≥ 0.8 B

(6.1)

where: ΔA = lateral deflection calculated from the truss frame (Frame A) alone ΔB = lateral deflection calculated from the simple frame (Frame B) alone

6.1.5 Sway Versus Nonsway Frames

A frame can be classified as nonsway if its response to in-plane horizontal forces is sufficiently stiff for it to be acceptable to neglect any additional internal forces or moments arising from horizontal displacements of the frame. In the design of a multistory building frame, it is convenient to

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isolate the columns from the frame and treat the stability of columns and the stability of frames as independent from each other. For a column in a braced frame, it is assumed the columns are prevented from horizontal displacements at their ends and therefore are only subjected to end moments and axial loads. It is then assumed that the frame, possibly by means of a bracing system, satisfies global stability checks and that the global stability of the frame does not affect column behavior. This gives the commonly assumed nonsway frame. The design of columns in a nonsway frame follows the conventional beam-column capacity check approach, and the column effective length may be evaluated based on the column end-restraint conditions. Another reason for defining sway and nonsway frames is the need to adopt conventional analyses in which all the internal forces are computed based on the undeformed geometry of the structure. This assumption is valid if second-order effects are negligible. When there is an interaction between overall frame stability and column stability, it is impossible to isolate the column. The column and the frame have to act interactively in a sway mode. The design of sway frames has to consider the frame subassemblage or the structure as a whole. Moreover, the presence of inelasticity in the columns will render some doubts about the use of the familiar concept, elastic effective length (Liew et al., 1991, 1992). Based on the above considerations, a definition can be established for sway and nonsway frames as: A frame can be classified as nonsway if its response to in-plane horizontal forces is sufficiently stiff for it to be acceptably accurate to neglect any additional internal forces or moments arising from horizontal displacements of its nodes.

Section 5.2 of Eurocode 3 (CEN, 1992) provides some guidelines to distinguish between sway and nonsway frames. It states that a frame may be classified as nonsway for a given load case if Pcr / P ≥ 10 for that load case where Pcr is the elastic critical buckling value for sway buckling and P is the design value of the total vertical load. When the system buckling load factor is ten times more than the design load factor, the frame is said to be stiff enough to resist lateral load and is unlikely to be sensitive to side-sway deflections. AISC (1993) does not give specific guidance on frame classification. However, for frames to be classified as nonsway in AISC LRFD format, the moment amplification factor B2 has to be small (a possible range is B2 ≤ 1.10 ) so that sway deflection would have negligible influence on the final value obtained from the beam-column capacity check.

6.1.6 Joint Representation

The Load and Resistance Factored Design Specification for Structural Steel Buildings of the American Institute of Steel Construction (AISC, 2001) classifies two types of constructions: Type FR (Fully Restrained) and Type PR (Partially Restrained). Type PR comprises two cases, depending on whether connection restraint is ignored. If it is ignored, the connection is called a simple connection. When the connection restraint is considered, it requires that the strength, stiffness, and ductility characteristic of the connection be incorporated into the analysis and design. The assumptions used in the analysis and design of the framing systems shall be consistent with the performance characteristics of the connections. The European standard on Design of Steel Structures or Eurocode 3 Section 5.2 (CEN, 1992) defines three framing types: simple, continuous, and semi-continuous. The standard precisely distinguishes between these three types of connections and also recognizes that the extent of semi-rigid action depends to a large extent on the type of structure, such as braced or unbraced and sway or nonsway frames. Typical moment-rotation (M-θr) curves for beam-to-column connections are available from several databases: Goverdhan (1983), Ang and Morris (1984), Nethercot (1985), and Kishi and Chen (1986). Care should be


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exercised when using tabulated M-θr curves not to extrapolate to sizes or conditions beyond those used to develop the database. When the connections to be modeled fall outside the range of the databases, it may be possible to derive them from tests, simple component modeling, or finite element studies. Examples of how to model connection behavior are given in numerous references such as Bjorhovde et al. (1988, 1990, 1992, 1996), Chen and Lui (1991), Liew et al. (1991, 1992), Lorenz et al. (1993), Chen and Toma (1994), Chen et al. (1996), and Leon et al. (1996).

6.1.6.1 Joint Classification

The purpose of joint classification is to select a suitable basis on which to conduct the frame analysis and design. Based on stiffness and strength of a joint, the criteria presented in the next three sections may be adopted. 6.1.6.1.1 Rotation Stiffness Because the nonlinear behavior of the connection manifests even at low force levels, the initial stiffness of the connection Rki does not adequately characterize connection response at service levels. The secant stiffness Rks at service loads should be used. For a fully rigid connection, the connecting elements shall have sufficient strength and stiffness to effectively maintain the angles between intersecting members under the design loads. The secant rotational stiffness of the fully rigid connection at the service load level shall exceed 20EIb /Lb of the beam. For simple connections, the secant rotational stiffness at the service load level shall not exceed 2EIb /Lb of the beam. A semi-rigid beam-to-column connection shall have sufficient rotation capacity to avoid overloading the connecting elements, fasteners, or welds under the design loads. 6.1.6.1.2 Moment Capacity The strength of a connection can be determined based on an ultimate limit-state model of the connection or from a physical test. If the moment–rotation response does not exhibit a peak load, then the strength can be taken as the moment at a rotation of 0.02 radians (Leon et al., 1996). The flexural strength of a full strength connection shall exceed the moment capacity of the beam. Connections that transmit less than 20 percent beam flexural capacity at a rotation of 0.02 may be generally classified as a simple connection. Connection with flexural capacity that falls within 20 percent and 80 percent of the moment capacity of the beam is called a partial strength connection. 6.1.6.1.3 Ductility Requirement If the connection strength exceeds the beam section strength, then the ductility of the structural system is controlled by the beam and the connection can be considered elastic. If the beam strength exceeds the connection strength, then deformations can concentrate in the connection. The ductility required of a connection will depend on the particular application. For example, the ductility requirement for a braced frame in a nonseismic region will generally be less than the ductility required in a high seismic region. The rotation capacity can be defined as the value of the connection rotation at the point where either (a) the resisting strength of the connection has dropped to 80 percent of the peak moment capacity or (b) the connection has deformed beyond 0.03 radians. Criterion (b) is intended to apply to ductile connections where there is no strength drop until the occurrence of large rotations. The available rotation capacity should be compared with the rotation required under the full factored loads as determined by an analysis that takes into account the nonlinear behavior of the connection. In the absence of an accurate analysis, a rotation capacity of 0.03 radians is considered adequate. This rotation is equal to the minimum beam-to-column connection capacity as specified in the AISC seismic provisions for special moment frames.

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6.1.7 Analysis and Design of Semi-rigid Frames

As discussed in the previous sections, the three types of framing are the simple, rigid (continuous), and semi-rigid (semicontinuous) framings corresponding to where pinned-joint, rigid-joint, and semi-rigid joint models are adopted, respectively. Joints represented as rigid or pinned in the analysis must be designed to satisfy the rigid joint and nominally pinned joint classifications, respectively. The semi-rigid model can be more or less sophisticated. Joints can be modeled as spiral springs having moment-rotational relationships that can range from the linear-elastic type to the nonlinear type, which allows for the degree of ductility of the joints. The use of a linear-elastic global analysis model requires that the joint behavior be modeled as being linear-elastic also. For an elastic perfectly plastic analysis, a bilinear joint model is needed. Therefore, the type of analysis used has a direct impact on the degree of complexity of the joint model to be adopted, particularly when plastic analysis is used and hinges are allowed to occur in the joints. A nonlinear joint modeling means that the results for different analysis cannot be superimposed. When a joint is classified as semi-rigid or partial strength, the relevant response characteristics of the joint should be included in the analysis of the structure to determine the member and connection forces, displacements, and frame stability. An analysis that incorporates semi-rigid joint deformations must include consideration of:

1. Joint initial stiffness, rotation capacity, ductility, and energy absorption capability; these are critical factors for many structures, including rigidly joined frames. These factors are especially important for structures located in seismic regions. 2. Serviceability of the structure and its joints; the prime considerations here are the deformations and other stiffness-related characteristics of the joints, and their effects on the service load deformations of the frame. 3. Strength and stability of the frame and its component members; the effects of partial joint restraint on the ultimate strengths of the members and frame should be considered. The structure is acceptable with respect to strength if the nominal resistance of the structure is greater than the factored load effects.

The degree of sophistication of the analysis depends on the problem at hand. Usually, the design of semi-rigid frames requires separate analyses for the serviceability and ultimate-limit states. For serviceability, an analysis using linear springs with initial stiffness at a service load level is sufficient if the resistance demanded of the joint is well below the strength. Under factored loads, a more careful procedure is needed to ensure that the characteristics assumed in the analysis are consistent with those of the joint response. The response is especially nonlinear as the applied moment approaches the joint strength. In particular, the effect of the joint nonlinearity on second-order moments and other stability checks needs to be considered. A design procedure for semi-rigid frames based on advanced inelastic analysis is proposed below:

1. Perform preliminary analysis and design steps. The preliminary analysis should be carried out assuming rigid frame action. The magnitude of moment to be resisted at the beam ends may be estimated based on the gravity load combination. The engineer might use first-order elastic or plastic analysis with amplification factors, second-order elastic analysis, or any other technique judged to be appropriate in this preliminary stage of design. 2. Select the type of semi-rigid joint to be used in the construction. For example, the beamto-column connection could be any type of standard connection, such as double web angles, single web angles, top-and-seat angles with or without double web angles, header


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plates, flushed or extended end plates, etc. Based on the information in Step 1, make an initial guess of the various dimensions and thicknesses of the connecting material, and check the connections for the second-order moments by calculating the bolt tension, bolt shear, and stresses in the connecting angles, etc. 3. Determine the ultimate moment capacity and initial stiffness of the joint. The approximated shape of the M-θr curve of the joint should be known in advance. Since the currently available data do not include all conceivable types of connections, it is advisable to restrict connection designs to those for which M-θr curves have been well established. 4. Check the joints for ductility. In essence, this requires that all connection materials such as bolts, welds, and plates should not be loaded beyond the resisting strengths under the simultaneous actions of factored gravity and wind loads. 5. Perform second-order inelastic analysis incorporating the effects of semi-rigid joints in the factored load analysis. 6. Check strength-limit states. The structure is said to be satisfactory if its nominal resistance is greater than the factored load effects. 7. Check for serviceability limit states to ensure adequate stiffness for functionality at service loads. 8. Since the preliminary design is based on the assumption that joints are fully rigid, Steps 1 and 2 may yield a conservative design. The joint designs can be modified if the design resistance of the structure is greater than the factored load effects. Alternatively, the member sizes may be adjusted to provide a more efficient design. Iteration of Steps 2–8 gives results that will converge to the most cost effective design satisfying the various design constraints imposed on the analysis.

6.1.8 Frame Stability

There are many parameters and behavioral effects that influence stability of steel-framed structures. The extent to which these factors are modeled in analysis will affect the criteria that one applies in design of the frame, its members, and joints. Three basic aspects of behavioral effects due to geometric and material nonlinearities and initial imperfection will ultimately govern frame deformations under applied loads and the resulting internal load effects.

6.1.8.1 Imperfection Effects

Modern stability design provisions are based on the premise that the member forces are calculated by second-order elastic analyses, where equilibrium is satisfied on the deformed structure. When stability effects are significant, consideration must be given to member initial imperfections. Many code provisions for calibrating the stability requirements are based on initial geometric imperfections conservatively assumed as equal to the maximum fabrication and erection tolerances permitted by the code. For columns and frames, this would normally imply a member out-of-straightness equal to 0.001L where L is the member length between brace or framing points, and a frame out-of-plumb equal to 0.002H where H is the story height. Many of the code’s specified analysis and design approaches are calibrated against inelastic distributed-plasticity analyses that account for yielding through the member cross-section and along the member length. Thermal residual stresses in I- or H- (wide flange) shape members are assumed to have maximum values of 0.3fy, which are linearly varying across the flanges and uniform tension in the web. Detailed behavioral effects for frame analysis and design are shown in Table 6.1.

152


TABLE 6.1 Behavioral effects for frame analysis and design 1. Geometrical nonlinear effects • Geometric interaction due to axial, flexural, torsional and warping deformations • P-Δ effect: effect of axial force acting through the relative horizontal displacements associated with member chord rotation • P-δ effect: effect of axial force acting through displacements associated with member curvature • Sway shortening: effect of large chord rotation on longitudinal displacements at member ends • Curvature shortening (bowing effect): effect of curvature on axial displacements at member ends • Initial out-of-straightness of member • Initial out-of-plumbness of frame • Behavior of moments under finite three-dimensional rotations • Diaphragm action • Finite joint size and panel zone deformation 2. Material nonlinear effects • Zero-length plastic hinge

º elastic-plastic º elastic unloading º elasto-plastic º strain hardening

• Spread-of-plasticity in members • Inelastic interaction

º axial force and biaxial bending º axial force, biaxial bending and warping

• Connection flexibility

• Composite action from floor slabs • Walls and infilling • Initial residual stresses • Local buckling and distortions • Shear yielding • Cyclic plasticity effects 3. Loading effects • Proportional or non-proportional loading • Variable repeated loading • Dynamic loading


153

6.1.8.2 Limit States Design

Member strength may be controlled by any one of the following limit states: cross-section yielding, local buckling, flexural buckling, and torsional-flexural buckling. Most of the structural analyses envisioned for routine design use do not model limit states associated with local buckling of cross-section or torsional-flexural buckling of members. Therefore, these limits must be considered in separate member design checks. For inelastic analyses, the effect of cross-section yielding is incorporated directly in the analysis. For elastic analyses, the cross-section strength can be checked by an interaction equation that approximates the P-M yield surface. The ability of the analysis to capture in-plane flexural buckling depends on the extent to which the maximum moments are affected by distributed plasticity and member imperfections. Concerns regarding the ability of the analysis to capture these effects suggest the need to apply a member check for in-plane flexural buckling, even when an accurate second-order analysis is used. A major consideration for the in-plane flexural buckling check relates to the assumed buckling length used in calculating the design compression strength.

6.1.8.3 Second-order Analysis

In practice, there are alternative approaches one can employ for conducting second-order analyses, some of which are more rigorous than others. The difference between simplified and rigorous analyses depends on the extent to which P-δ effects due to curvature of the member relative to its chord are modeled and whether the problem is linearized to expedite the solution. Rigorous second-order analyses are those that accurately model all significant second-order effects such as to include the solution for the governing differential equation either through stability functions or computer frame analysis programs that model these effects. Not all modern commercial computer programs are capable of rigorous analyses. Methods that modify first-order analysis results through second-order amplifiers are in some cases accurate enough to constitute a rigorous analysis, but this depends on the magnitude of second-order effects and other characteristics of the problem. A common type of approximate analyses are those which capture only P-Δ due to member end translations (e.g., interstory drift) and fail to capture P-δ effects. Where P-δ effects are significant, errors arise in approximate methods that do not accurately account for the effect of P-δ moments on amplification of both local member moments and the calculated global displacements.

6.1.8.4 Direct Analysis Approach

The direct analysis approach is developed with the goal to accurately model frame stability effects, and thereby eliminate the need for calculating effective buckling lengths for column designs. The new provisions in the AISC Specification (2005) involve reducing the nominal elastic stiffness and applying a notional load to the frame. The notional load approach can be found in steel standards such as Eurocode 3 Section 5.2 (CEN, 1992), but many aspects of the proposed provisions given in the new AISC Specification (2005) address known shortcomings of conventional notional load approaches in other standards. In the reduced stiffness approach, the reduction on the flexural stiffness EI can be applied by modifying E in the analysis. For computer programs that perform semiautomated design checks, one should be sure that the elastic modulus is not reduced in design equations that involve E to evaluate the design strength. The reduced stiffness and notional load requirements only pertain to analysis of the strength-limit state, but do not apply to analyses of other serviceability conditions. Notional load is applied to represent the destabilizing effect of a geometric imperfection and other effects such as yielding, nonidealized boundary, loading conditions, etc. Notional loads are

154


applied as lateral loads at each floor level and are specified in terms of the gravity loads applied at that floor level. The notional load magnitude of 0.002 corresponds to a frame out-of-plumb equal to 0.002H (where H is the story height). Notional loads shall be applied in the direction that adds to the destabilizing effects under the specified strength load combination. Sections 6.2 and 6.3 of this chapter deal with detailed modeling of steel and composite semirigid frames with an aim to apply direct analysis for frame design.

6.2 Advanced Analysis of Steel Frames 6.2.1 Development of Advanced Analysis

6.2.1.1 Assessment Approaches for Strength and Stability

For decades, structural engineers and researchers have been exploring various approaches for assessing the member and frame stability in the design of frame structures. Figure 6.5 shows the load-deflection curves of a rigid sway frame generated by various analysis methods (White and Chen, 1993; Chan, 2001). The basic distinctions between the analysis methods represented by each curve are (1) whether equilibrium is satisfied on the deformed or undeformed geometry of the structure, and (2) whether material remains elastic or inelastic. First-order elastic analysis provides a simple estimate of the distribution of forces within the structural system. However, it does not provide any information about the influence of either plasticity or stability effects on the behavior of the frame. Second-order elastic analysis, which is the preferred method in AISC (2001), is formulated based on the deformed configuration of the structure. It can account for elastic stability effects, but it does not provide any direct information on the actual inelastic strength of the frame. Therefore, in most contemporary design standards for frame structures, the combined stability and

Load Ratio, λ

λcr

Elastic Buckling Load

Elastic Stability Limit Load

First-Order Elastic Analysis

Rigid Plastic Analysis

Second-Order Elastic Analysis First-Order Elastic-Plastic Analysis

λp

Plastic Limit Load

Inelastic Stability Limit Load

λH λH

Local and/or LateralTorsional Buckling

Second-Order Inelastic Analysis

Lateral Deflection, ∆ FIGURE 6.5 Types of analyses (White and Chen, 1993).

λw λw

∆


155

plasticity effects are considered indirectly through strength and stability criteria for beam-columns. Devices such as column effective length factors and notional loads are commonly used to approximate the member-frame interactions. However, such approaches usually introduce simplifying behavioral assumptions such as artificial distinctions between braced and unbraced frames, the likelihood of all columns in a story failing simultaneously, and the combination of inplane and out-of-plane member stability effects. Bifurcation analysis ignores the prebuckling deformation, initial imperfection, and material yielding and assumes a sudden interception of a secondary equilibrium path to the primary path. It performs the eigenvalue analysis to obtain the elastic buckling load, which represents an upper bound solution. Rigid plastic analysis considers material yielding concentrating at zero length plastic hinges and ignores instability and large deflections. The plastic-limit load with assumed collapse mechanisms is obtained by equalizing the external work done to the internal strain energy for the most critical collapse mechanism. Merchant (1954) considered both the effects of yielding and buckling approximately by using the Merchant-Rankine formula obtained from the elastic buckling and plastic-limit load factors. Second-order inelastic analysis considers the combined effects of stability and plasticity. The inelastic effects may be handled by techniques ranging from the simple elastic-plastic-hinge model to the more refined inelastic models, which can include the spread-of-plasticity or distributed plasticity effects. Subject to limitations of the behavioral effect considered in the analysis and accurate modeling of inelastic force redistribution, the limit load obtained by a second-order inelastic analysis is the most accurate representation to the true strength of the frame.

6.2.1.2 Direct Analysis of Frame’s Stability and Strength

With the advancement of computer technology in recent decades, advanced analysis method has been fully developed for the design used in the steel construction (Chen and Toma, 1994; Chen et al., 1996; White, 1996; Chen and Kim, 1997; Liew et al., 2000a; Chen, 2008). Advanced analysis is defined as a method of second-order inelastic analysis that sufficiently represents the behavioral effects associated with member primary limit states such that separate member capacity checks are not required. When properly formulated, calibrated, and executed, the advanced analysis can rigorously assess the strength and stability interdependence of the member and system, the actual failure mode, and the maximum strength of the structural system. Table 6.1 provides a summary of the behavioral phenomena and physical attributes that may be considered in the nonlinear analysis of frame members, either by explicit or implicit means (Ziemian, 1990; White and Chen, 1993; Chen et al., 1996; White, 1996). For an analysis method to be classified as advanced, not all of the behaviors need to be addressed or represented in the design and analysis situation. When certain attributions cannot be considered in the analysis, they may be viewed as the limitations of the analysis model, and these limitations must be considered in the final design. For example, at the current stage, most advanced analysis packages based on one or least elements per member are unable to model the more complex aspects of member behavior that involves inelastic lateral-torsional buckling and local buckling, which may significantly reduce the maximum load-carrying capacity of the structure (see Figure 6.5). Therefore, most practical approaches for stability design still require the separation of in-plane frame and member behavior from out-of-plane member stability checks. The members’ slenderness ratios must be checked to ensure that inelastic lateral-torsional buckling does not occur. Additional checks are required to ensure that local buckling does not occur and that cross-sections have adequate rotation capacity to allow inelastic redistribution of forces between the frame members. The theory and approaches for advanced analysis of plane frames composed of members with compact sections—fully braced out-of-plane—have been well developed (Chen and Toma, 1994;

156


Chen et al., 1996; Chen and Kim, 1997). Experimental calibration frames and numerical results from accurate distributed analyses are available to verify the advanced analysis (Chen and Toma, 1994; Toma et al. 1995; Liew et al., 1997b; Surovek, 2007). Thus, it is feasible to model inelastic member and frame stability directly in a single analysis of planar frames. Research on frames with semi-rigid connections has advanced to a stage where practical tools exist for application in design (Hsieh and Deierlein, 1991; Chen et al., 1996). Numerical tools for secondorder inelastic analysis of 3-D frames have been developed and proposed by Orbison (1982), Ziemian et al. (1992), Chen et al. (2000), Liew et al. (2000b), Kim et al. (2001), and Liew and Chen (2004a). The Australian Standard (AS4100, 1990) and Eurocode 3 (CEN, 1992) explicitly permit the checking of in-plane member and frame stability based solely on the advanced analysis. In the 2005 AISC Specification, steps have been taken to allow designers to more explicitly assess the strength of steel structures. The most recent edition of the AISC Specification (AISC, 2005) in Appendix 7 includes a new method of analysis and design termed the direct analysis method, which permits the checking of steel frame strength accounting explicitly the key phenomena that affect the system and member strengths. By incorporating a nominal outof-plumbness and a nominal stiffness reduction in the structural analysis, the direct analysis method eliminates the need to calculate and apply column effective length, and provides a direct path from elastic analysis and design to advanced analysis (Liew and Chen, 2004a; Lui and Ma, 2005; White et al., 2006; Surovek, 2007). The primary benefits in directly assessing the capacity of a structure within the analysis is that it allows for a simplified design methodology that eliminates the need to check certain member interaction equations and determination of design approximations such as effective length factors. Furthermore, the member and system behavior can be directly assessed and hence can be tuned to better achieve design objectives. The advanced analysis provides better insight into the structural behavior up to failure by observing the load-displacement characteristic of the structure and the sequence of hinge formation in the frame. It is particularly useful for flexible and nonsymmetrical structures. The enhanced understanding of behavior provided by the advanced analysis improves the designer’s ability to place materials where they are most effective. The evaluation of a system’s limit state will provide a more uniform safety level compared to the conventional approach based on first member failure. Moreover, design economy can be realized if a higher proportion of the inelastic reserved strength built into the system can be utilized in design. There is a worldwide trend for modern design specifications to depart from prescriptive methods and to move toward performance-based design approaches (Liew and Chen, 2004a). The gradual shift towards performance-based design increases the need to have efficient and robust nonlinear inelastic analysis methods to assess the global performance of structures. There is a logical relationship between this design approach and the use of advanced analysis method because the direction of performance-based design is to move away from prescriptive design equation checks of specification. With the advanced analysis method, a structural engineer can now introduce the concept of structural fuse in his design process (Chen, 2000). These fuses can be designed to fail under extreme loads, while leaving the majority of the connections in satisfactory condition. One type of the fuses is the reduced beam section configuration, in which a portion of beam flanges near the beam-to-column joint is cut to allow a plastic hinge to form away from the joint. By using the advanced analysis, these structural fuses can be strategically located throughout a structure without the risk of the building, as a whole, falling down. This would not only limit the amount of post-quake repair, but would also indicate where the failed connections were and thus greatly reduce the expense of inspection procedures.


157

6.2.1.3 Application to Tubular Structures

The quest for oil and gas exploitation has been pushing the development of offshore platforms such as jackets and jackups that can operate in deeper and harsher water. During operation, offshore platforms are subjected to extreme loads caused by waves, currents, hurricanes, and earthquakes. Over the years, catastrophic events such as explosions, fires, ship impacts, and dropped objects have resulted in the increased focus on the structural resistance to accidental events. A rational evaluation of the structural strength considering these factors would require all the nonlinear effects to be taken directly into the analysis. Amdahl et al. (1994), Hellan (1995), and Skallerud and Amdahl (2002) proposed methodologies for nonlinear analysis of 3-D tubular structures covering three main aspects: (1) basic nonlinear continuum mechanics and numerical procedures implemented in state-of-the-art computer codes, USFOS (Søreide et al., 1994; USFOS, 2009); (2) modeling of nonlinear tubular joint and member behavior on 3-D behavior and collapse mechanisms; (3) reserved and residual strength of 3-D frames and the redundancy and load-shedding characteristics system behavior. Their works, which includes many of the recent developments in assessing the capacity of offshore structures, have been adopted by DNV into the standard DNV-RP-C204 (2004). DNV, SINTEF, and BOMEL carried out the ULTIGUIDE project (1999) to provide best practical guidance for engineers to select parameters and interpret results from a nonlinear analysis. The guide, which focuses on jacket structures, does not specify a recommended safety level, but is intended for use with existing codes and specifications. The topics covered in this guide address the question arising in connection with reassessment of existing structures, but the recommendations will be valid also in other design situations. ICSS committee III.1 provides a summary report Ultimate Strength (2006) about the research progress on the ultimate strength of tubular members and joints, plates and stiffened plates, shells, ship structures, offshore structures, composite structures, aluminum structures, and relevant benchmarks in the International Ship and Offshore Structures Congress held every three years. Experiments were carried out to benchmark the nonlinear analysis methods. To understand the frame cyclic inelastic behavior, which determines the survivability of the offshore structures in the event of severe seismic ground excitations, Zayas et al. (1980) carried out the first large scale frame test for two one-sixth scale two-dimensional (2-D) X-braced double-bay frames, which stand more than 8m high under cyclic loading. The Jointed Industry Project (JIP) organized by BOMEL and other organizations investigates experimentally two series of 2-D large scale frames which consist of six X-braced two-bay frames and four K-braced single-bay frames, both under static loading (BOMEL, 1992). The subsequent phase of the JIP (Bolt and Billington, 2000) tests one large-scale 3-D frame under a series of static loading conditions. These are by far the largest frames tested worldwide. The findings indicated that within the confines of a frame, the structural component behaves differently than isolated tests on an individual component, on which engineering practice has been based. Furthermore, both analyses and tests have shown that structural systems exhibit significant reserve strength beyond design load levels. Besides, Qian (2005) and Choo et al. (2005) carried out research to extend the understanding to the thickwalled joints and developed a nonlinear joint model for the ultimate strength frame analysis of offshore structures.

6.2.2 Stiffness Formulation of Beam-column 6.2.2.1 Available Stiffness Formulations

Two popular methods have been used to derive the tangent stiffness matrix of a beam-column element, i.e., the beam-column approach and the finite element approach. The beam-column approach was originally proposed by Oran (1973), later improved by Kassimali and Abbasnia (1991)

158


to include the effect of axial force on the torsional stiffness and some coupling stiffness terms, and recently by Chan and Gu (2000) to include the effect of the member initial out-of-straightness. In this approach, the tangent stiffness matrix is derived from the member basic force and deformation within the secant relationship, which satisfies the fourth-order beam-column equilibrium equation. The initial undeformed chord, which translates and rotates as a rigid body, is selected as the reference configuration and the member bowing effect can be captured. Chan and Zhou (1995) expressed their member force and deformation in the form similar to Chan and Gu (2000), and considered the bowing effect and member initial out-of-straightness. The stability and bowing functions in Chan and Zhou (1995) is based on the fifth-order polynomials, which can be used to approximate the accurate values of Chan and Gu (2000) with high accuracy. However, when an attempt is made to solve for the 3-D frame behavior, i.e., a direct extension is made from planar element to space frame element, some coupling terms between the flexural and torsional displacements are lost in the four aforementioned methods. Therefore, the lateral-torsional buckling cannot be predicted by using such an approach. The other method is the finite element approach by using the cubic interpolation functions for lateral displacements (Orbison, 1982; Izzuddin and Elnashai, 1993a; Yang and Kuo, 1994). Since the stability criterion is based on the principles of energy, it eliminates the necessity of going through the seemingly ad hoc visualization required to account for changes in geometry when formulating the beam-column equilibrium equations for free-body diagrams. This approach can be extended to a wide range of problems, such as the 3-D inelastic analysis. Since the energy principles are able to define the nonlinear coupling between compression, bending, and torsion, the derived element can be used to predict the axial-torsional and lateral-torsional buckling, which are essential for an accurate estimate of the second-order effect in 3-D framework. However, the pitfall of using the cubic interpolation function approach is that one cubic element cannot be used to predict accurately the flexural buckling load of columns unless more elements per physical member are used. Since the straight, albeit stressed, element has been widely adopted in the element stiffness formulation, the frame members have to be subdivided into several elements to capture the member bowing effect in the nonlinear analysis. This will inevitably increase the complexity of structural modeling and the cost and time of computation. To avoid the limitations of the beam-column approach and the cubic element approach, a 3-D beam-column element has been developed by using the stability interpolation functions that satisfy the fourth-order differential equation of beam-columns (Liew et al., 2000b). The flexural buckling load of columns and frames can be captured with one element per member. With some modifications, the proposed beam-column element considers the member bowing effect and initial out-of-straightness. Hence, the nonlinear behavior of frames composed of slender member subject to high axial force can be captured with less elements per member. The advantages of the proposed beam-column formulation over the conventional beam-column approach and the cubic element approach are highlighted by numerical examples given in Liew et al. (2000b). Besides the beam-column approach and finite element approach, Yang et al. (2002) recently developed a methodologically new, physically interpretable approach for formulating the beam element using the equilibrium approach—called direct approach—by adhering strictly to the assumption of small strains, small displacement, and small rotations for each incremental step of nonlinear analysis.

6.2.2.2 Virtual Work Equation

In the incremental finite element analysis, three formulations are popularly used to derive the element stiffness, i.e., the Updated Lagrangian (UL) formulation, the Total Lagrangian (TL) formulation, and the Co-Rotational (CR) approach. In the UL formulation, the motion of element is described based on the previous (known) deformed configuration. Whereas, in the TL formulation, the motion of element is described based on the initial undeformed configuration. It has


159

been concluded by Bathe and Bolourchi (1979) that the UL formulation is computationally more efficient than the TL formulation for frame structures. On the other hand, the reference configuration in a CR formulation continuously translates and rotates with the element, but does not deform with it (Teh and Clarke, 1996, 1998). The CR formulation was also called the Co-Rational Total Lagrangian formulation in Teh and Clarke (1996), the Eulerian formulation in Izzuddin and Elnashai (1993b) due to the co-rotational but undeformed reference configuration. The CR formulation has certain advantages such as reduction in degrees-of-freedom involved in the formulation by excluding the rigid body modes and volume integrations generally performed over the simple undeformed shape of the element. However, in the CR formulation, the approximate cubic interpolation functions for lateral displacement are normally adopted and special considerations should be taken to get the correct stability matrix. Considering the above reasons, the motion of a beam-column element is described based on the UL formulation as shown in Figure 6.6, with C0 representing the initial undeformed configuration, C1 the previous (known) deformed equilibrium configuration, and C2 the current (desired) deformed equilibrium configuration. The straight, albeit stressed, element at configuration C1 has been widely adopted in the stiffness formulation. Hence, in the range of large deflection, the frame members have to be subdivided into several elements to capture the member bowing effect. Gattass and Abel (1987a) developed a 2-D curved beam-column element based on the curved and stressed element configuration. However, due to the complicated symbolic operations, an extension to a 3-D case is difficult. 2y

C2 : incremental configuration

t + ∆t 2z

a 2L 1y

t 1z

t=0 0z

0L

a

C1 : deformed configuration

a 1L

0y

2x

b

b

1x

straight albeit stressed C0 : initial configuration element assumed

b

0x

Z

Y

X Global coordinate system FIGURE 6.6 Motion of a beam-column element based on the UL formulation.

160


In the finite element approach, the element stiffness can be derived using either the principle of potential energy or the principle of virtual work. The principle of virtual work has advantages over the principle of potential energy in that it is not restricted to material laws or loading type and can consider the geometric nonlinearities easily by including the nonlinear strain components in the increment Lagarangian formulations (Yang and Kuo, 1994). Based on the principle of virtual work, the following equation can be written for an element in an incremental sense between the previous configuration C1 and the current configuration C2:

∫

1

∫

1

1

V

1

V

Cijkl 1 ekl δ 1 eij 1dV + C

ijkl

Cijkl 1 ηkl δ 1 eij 1dV + ∫ 1 ijkl 1 kl δ 1 ηij 1 + 1 V V 1V C e dV 1 1 1 T 2 1 η δ η dV + τ δ η dV = δ u f − f 1 1 1 1 kl 1 ij ∫ 1 ij 1 ij j

∫

1

(

1

V

(6.2)

)

in which 1 Cijkl is the incremental constitutive tensor; 1eif and 1ηif are the linear and nonlinear components of Green incremental strain tensor, respectively; 11τ ij is Cauchy stress tensor; u is element displacement vector; and f is the element force vector. In Equation 6.2, a left subscript in a symbol denotes the configuration in which the quantity is measured. A left superscript denotes the configuration in which the quantity occurs. The absence of a superscript means that the quantity is an increment between configurations C1 and C2. If cubic interpolation functions are used for lateral displacements, the first term in the left side of Equation 6.2 yields the elastic stiffness matrix, and the fifth term yields the geometric stiffness matrix. The second to the fourth terms yield higher-order stiffness matrices, which have been considered by Yang and Leu (1994) for planar frame using the principle of virtual work, and by Chajes and Churchill (1987) for planar frame using the principle of potential energy. The third higher-order term has been considered by Al-Bermani and Kitipornchai (1990) for deriving the stiffness matrix of a 3-D beam element with thin-walled sections. However, inconsistent reference configurations were used for nodal displacements with translations referred to C1 and rotations referred to C2 as pointed out by Teh and Clarke (1996). Jiang et al. (2002) considered the first to the fifth terms in the left side of Equation 6.2 in their plastic zone analysis. However, the stiffness matrix is not given in explicit form, whereas it is integrated numerically. Figure 6.7 shows the beam-column element with twelve degrees of freedom. The local coordinate is chosen with the x axis as the centroidal axis, and the y and z axes as the principal axes. There are six stress resultants at each end: three forces, Fx, Fy, and Fz; three moments, Mx, My, and y

Mxa Fxa θxa ua

Myb, θyb

Mya, θya Fya, va a

Fyb, vb b Fzb, wb

Fza, wa z

Fxb Mxb ub θxb

Mzb, θzb

Mza, θza L

FIGURE 6.7 Force and displacement components of a beam-column element.

x


161

Mz. The corresponding displacements are translations u, v, and w; and rotations, θx, θy, and θz. The basic assumptions used in modeling the beam-column element are:

1. Elements are initially prismatic and cross-sections do not distort. 2. Plane sections remain plane after deformation. 3. Local buckling is not considered and all members are assumed to be compact. 4. Warping, shear, and inelastic torsional deformations are neglected. 5. Member deformations with respect to the chord length are assumed to be small, but global displacements and rotations can be moderately large.

Assumption 5 requires the rotational angles between the tangent at the member ends and the chord joining the two member ends to be small (see Figure 6.8). If this assumption is violated, the member should be divided into two or more elements to reduce the magnitude of the rotational angle. However, this condition is seldom encountered in practical structures. By adopting the assumptions of beam-column and ignoring the second to the fourth terms on the left side of Equation 6.2 the linearized form of an incremental virtual work equation may be expressed as: 1 L EAδ u ′ 2 + EI zδ v ′′ 2 + EI yδ w ′′ 2 2 ∫0 L F L + ∫ x δ v ′ 2 + w ′ 2 dx − ∫  Fyδ ( u ′v ′ 0 0 2 L L − ∫  Fzδ ( v ′θ x + M yδ ( v ′θ x′  dx + ∫

( )

0

) )

)

(

)

0

Mx δ ( v ′w ′′ − δ ( v ′′w ′  dx = δ u T −∫  0 2  L

)

0.9 0.8

) + GJδ (θ ′ ) x

2

dx

) + F δ (u ′w ′ ) dx + ∫ K2 δ (θ ′ )  F δ ( w ′θ ) − M δ ( w ′θ ′ ) dx  

(

L

z

y

2

f − 1f

x

0

x

z

2

N3n

x

)

N3

0.7 0.6 0.5 0.4 0.3

N4n/L

0.2 0.1 0.0 0.0

N4/L 0.1

dx

P/Pe= 0 (cubic interpolation functions) P/Pe= 1 P/Pe= 2 P/Pe= 3

1.0

Stability interpolation functions for compression

(

( )

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Distance along the element length x/L FIGURE 6.8 Stability interpolation functions.

1.0

(6.3)

162


in which E is the elastic modulus; G is the shear modulus; L is the element length at configuration C1; A is the cross-sectional area; Iy and Iz, are moments of inertia, respectively; K = Fxb (Iy + Iz) is the Wagner coefficient; J is the torsional constant; and f and u are element force and displacement vectors given as:

f =  Fxa Fya Fza M xa M ya M za Fxb Fyb Fzb M xb M yb M z  T

u = ua va wa θ xa θ ya θ za ub vb wb θ xb θ yb θ zb 

T

zb

(6.4) (6.5)

The inclusion of the fourth integral in the left side of Equation 6.3 would lead to an accurate prediction of the axial-torsional instability of the column due to the Wagner effect. The inclusion of the fifth to the seventh integrals is important for predicting the lateral-torsional buckling.

6.2.2.3 Stability Interpolation Functions

The derivation of the element stiffness matrices is based on the displacement field assumed. Linear interpolation functions are adopted for the axial displacement u and the angle of twist θx. The stability interpolation functions are used for the lateral displacements v and w. The displacements at the centroid of an arbitrary cross-section can be written in terms of those at element ends: u = N u u

(6.6a)

v = N v u

(6.6b)

w = N w u

(6.6c)

θ x = N θ u

(6.6d)

where: N u =  N1 0 0 0 0 0 N 2 0 0 0 0 0 

(6.7a)

N v =  0 N 3z 0 0 0 N 4z 0 N 5z 0 0 0 N 6z  N w = [0 0 N 3y 0 − N 4y 0 0 0 N 5y 0 − N 6y 0]

N θ =  0 0 0 N1 0 0 0 0 0 N 2 0 0  The linear interpolation functions are given by:

(6.7b) (6.7c) (6.7d)

N1 = 1 − ξ

(6.8a)

N 2 = ξ

(6.8b)

in which ξ = x / L . The stability interpolation functions Nnz (where n = 3–6) can be derived from the fourth-order differential equation of a beam-column subject to the axial force P (P < 0 for compression, P > 0 for tension). Following the general procedures of the finite element formulation, the stability interpolation functions in both planes are assumed to be independent. The stability interpolation functions for compression members are given by:

N 3n =

1− c s s 1 − c − kLs cos ( k x − sin ( k x + k x + ∆ ∆ ∆ ∆

(6.9a)

N4n =

s − kLc 1 − c − kLs 1− c kLc − s cos ( kx + sin ( kx + kx + k∆ k∆ k∆ k∆−

(6.9b)

)

)

)

)


163

N 5n =

c −1 s s 1− c cos ( kx + sin ( kx − kx + ∆ ∆ ∆ ∆

(6.9c)

N6n =

kL − s c −1 1− c s − kL cos ( kx + sin ( kx + kx + k∆ k∆ k∆ k∆

(6.9d)

)

)

)

)

in which c = cos(kL), s = sin(kL), Δ = 2 − 2 cos(kL) − kL sin(kL), and k = P / EI n (n = y, z). The stability interpolation functions for tension members are given by:

N 3n =

N4n =

N 5n

N6n =

1− c s s 1 − c + kLs cosh ( kx + sinh ( kx − kx + ∆ ∆ ∆ ∆

)

)

s − kLc 1 − c + kLs 1− c kL cosh ( kx + sinh ( kx + kx + Lc − s k∆ k∆ k∆ k∆ c −1 s s 1− c = cosh ( kx − sinh ( kx + kx + ∆ ∆ ∆ ∆

)

)

)

)

kL − s c −1 1− c s − kL cosh ( kx + sinh ( kx + kx + k∆ k∆ k∆ k∆

)

)

(6.10a) (6.10b) (6.10c) (6.10d)

in which c = cosh(kL), s = sinh(kL), and Δ = 2 − 2 cosh(kL) − kL sinh(kL). If the axial force P is small, they can be approximated by the cubic interpolation functions that are independent of the axial force:

N 3 = 1 − 3ξ 2 + 2ξ 3

(

N 4 = L ξ − 2ξ + ξ

N 5 = 3ξ − 2ξ

N 6 = L −ξ 2 + ξ 3

3

2

(

3

3

)

)

(6.11a) (6.11b) (6.11c) (6.11d)

Figure 6.8 shows the comparisons of the cubic and stability interpolation functions. It can be seen that the errors for the cubic interpolation functions increase as the axial force increases. The main advantage of the stability interpolation functions is that they satisfy the governing differential equations of beam-column and thus can be used to predict accurately the lateral displacement under the effect of axial force (i.e., P-δ effect).

6.2.2.4 Elastic and Geometric Stiffness Matrices

The forces at the internal cross-section can be expressed in terms of those at the element ends:

Fx = Fxb

Fy = − ( M za + M zb ) / L

Fz = ( M ya + M yb ) / L

M x = M xb

M y = − (1 − ξ ) M ya + ξ M yb

)

M z = − (1 − ξ M za + ξ M zb

(6.12a) (6.12b) (6.12c) (6.12d) (6.12e) (6.12f)

164


Based on the displacement fields and the expression for the forces at the internal cross-section, the element stiffness matrix k can be derived from the virtual work equation as: 110 220 110 k = EA K uu + EI z K vv220 + EI y K ww + GJ Kθθ110 + Fxb K vv110 + xb ww 110 F K + + 110 − +K +KK K y

− −

(

uv

VM K+ M K ya

yb

L M za + M zb L

)

vu

(K (K

z

100 θ v

100 wθ

(

w u110

110

)

110 θθ

wu V Kw 111 + K + Kθ111 + M ya K v110 + Kθ110 + Kθ010 v v v θ vθ

+K

010 θw

+K

111 wθ

+K

M − xb K 120 + K 210 − K 2210 − K 120 2 wv vw wv vw

(

111 θw

)

(

)+ M ( K

)

za a

110 θ w

+ Kθ110 w

) )

(6.13)

where Vy = ( M za + M zb ) / L , Vz = ( M ya + M yb ) / L , and matrix K stv gh is given by:

K stv gh = ∫

d s N gT d t N h v x dx 0 dx s dx t

L

(6.14)

in which the subscripts g and h represent u, v, w, or θ; the superscripts s and t represent the order of differentiation of the vector of interpolation functions N; and v is the order of exponent to x. The tenth to the fourteenth stiffness terms on the right side of Equation 6.13 includes the coupling effects between the lateral and torsional displacements, which can be used to predict the lateral-torsional instability. If the cubic interpolation functions are used for the lateral displacements, the first to the fourth terms in the right side of Equation 6.13 will lead to the elastic stiffness matrix ke, and the remaining terms will result in the cubic geometric stiffness matrix kgc (Orbison, 1982; Yang and Kuo, 1994). If the stability interpolation functions are used for the lateral displacements, the first to the fourth terms on the right side of Equation 6.13 will contain terms that are functions of the axial force. The remaining terms must be evaluated together. Although the last term can be evaluated by using the stability interpolation function, the expressions are complex and not easy for use. For simplicity, the cubic interpolation functions are used instead. However, in evaluating the other terms, the stability interpolation functions for the lateral displacements are used consistently. The resulting element stiffness matrix k can be conceptually decomposed into two parts: the elastic stiffness matrix ke and the geometric stiffness matrix kg, based on the stability interpolation functions. The elastic stiffness matrix can be modified to consider the shear deformation (Przemieniecki, 1968), and is given in Appendix 1. The geometric stiffness matrix is given in Appendix 2. In the geometric stiffness matrix, the stability functions S1n and S2n, which account for the effect of axial force on the bending stiffness, are given by (Chen et al., 1996):

φn sin φn − φn2 cos φn  2 − 2 cos φn − φn sin φn S1n =  2  φn cosh φn φn sinh φn   2 −2 cosh φn − φn sinh φn  − 2 +  φn − φn sin φn  2 − 2 cos φ − φ sin φ n S2 n =  n 2 n s φ i φ − φn n n  inh  2 − 2 cosh φn + φn sinh φn

in which φn = L P / EI n and P = Fxb.

P< <0

P> >0

P<0 P>

0

(6.15)

(6.16)


165

If the axial force is small, they can be approximated as:

S1n = 4 +

2 PL2 15 EI n

(6.17)

S2 n = 2 −

PL2 30 EI n

(6.18)

Equations 6.17 and 6.18 can be called the third-order stability function because they can be derived if cubic interpolation functions are used for lateral displacement. It should be noted that the cubic interpolation functions involve some approximation for the lateral displacements, and its range of application must be understood. Defining the percent error in the element stiffness matrix terms as:  k − k Error =  c  × 100 (%)  k 

(6.19)

in which kc = ke + kgc and k = ke + kg are the element stiffness matrices based on the cubic and stability interpolation functions, respectively. The cubic geometric stiffness kgc can be obtained if Equation 6.17 and 6.18 are substituted into the geometric stiffness kg based on the stability interpolation functions. If |P/Pe| < 0.82 (Pe=π2EIn /L2 is the Euler’s load), the largest error in any of the terms of kc is less than 5 percent. If the cubic geometric stiffness matrix kgc is used for cases of |P/Pe| > 0.82, the corresponding members should be divided into two or more elements to limit the error in stiffness terms to less than 5 percent (White et al., 1993; Liew et al., 2000b).

6.2.2.5 Beam-column Approach and Member Bowing Effect

In the updated Lagrangian approach, the assumption of straight, albeit stressed, element is widely adopted. It is difficult to account for the influence of displaced shape on the element stiffness, such as the curvature shortening effect (bowing effect) and member initial out-of-straightness. However, for slender members under high axial load and members that are loaded far into the postcollapse region, it is important to consider the bowing effect to capture the nonlinear behavior. Considering a member with initial out-of-straightness as shown in Figure 6.9, the member basic force and deformation relationship can be written as (Oran, 1973; Kassimali and Abbasnia, 1991; Chan and Gu, 2000): M na =

EI n L0

 δn   S1n Θ na + S2 n Θ nb + c0 n L   0 

(6.20a)

M nb =

EI n L0

 δn   S2 n Θ na + S1n Θ nb − c0 n L   0 

(6.20b)

(6.20c)

Mx =

GJ + Pr02 Θx L0

 e P = EA  +  L0

  b1n ( Θ na + Θ nb ∑ = ,  n z y

)

2

+ b2 n ( Θ na − Θ nb

)

2

+ bvsn

2  δ    δn Θ n − Θ ) + b  n    (6.20d) ( L0 na nb vvn  L0    

where Mna and Mnb (n = z, y) are end moments; Θna and Θnb are the total end rotations; Mx is the torsional moment; Θx is the total twist; P is the axial force; e is the relative axial displacement; L0 is the initial member length; r0 = ( I y + I z ) / A is the polar radius of gyration; S1n and S2n are the stability functions; δy and δz, are the values of initial out-of-straightness at the midspan in the z and y directions, which can be worked out based on the direction and total amplitude of initial

166


y MzA Mx

a P

Deformed curvature Θza

b Θzb

δz

Mx

a P

P, e

Mzb

x

Mx, Θx

L0/2

L0/2 MyA

Initial curvature

Myb

b

Θya

Θyb

δy

P, e

e

z

x

Mx, Θx

L = L0 + e FIGURE 6.9 Member basic forces and deformations.

out-of-straightness at the midspan; b1n and b2n are the bowing functions that consider the change of member chord length due to curvature shortening, given by Oran (1973): b1n = −

( S1n + S 2 n ) ( S2 n − 2 ) S2 n 8 ( S1n + S2 n )

b2 n =

(6.21)

8 qn

(6.22)

and stability function c0nand bowing function bvsn and bvvn, considering the effects of member initial out-of-straightness are given by Chan and Gu (2000):

 πφn3 sin φn  − 2 π − φn2 (1 − cos φn )  c0 n =  πφn3 sinh φn   π 2 + φ 2 ( cosh φ − 1) n n  bvsn =

bvvn = −

(

π 3 ( S1n − S2 n ) 4 b2 n c0 n 2 + S1n − S2 n π 2 + qn

(

π 2 qn 2π 3 + qn

(

(6.23)

P>0

)

(

P<0

)

(

4 π 2 + qn

)

2

(6.24)

)

) +

2π 3c0 n

(π

2

PL2 qn = 0 EI n

+ qn

+

4π 2 qn2 b2 n

) (π 2

2

+ qn

)

2

when axial force is zero, b1n = 1/40, b2n = 1/24, c0n = 0, bvsn = 2/π, bvvn = 0.

(6.25) (6.26)


167

The element tangent stiffness matrix can be determined as: k t = T T t T + N

(6.27)

in which T is a 12 × 6 transformation matrix relating the member basic forces to the element forces in the local coordinate N, a matrix accounting for the work done by the initial force and the translational displacements and t, the tangent stiffness matrix for member basic deformations given by:

tij =

∂ Si ∂ Si ∂ q + ∂ dj ∂ q ∂ dj

for i, j = 1  6

(6.28)

PL2 T T in which S =  M za M zb M ya M yb M x P  , d = Θ za Θ zb Θ ya Θ yb Θ x e  , q = 2 0 , and π EI I = Iy + Iz. The tangent stiffness matrix expressed by Equation 6.28 can be decomposed into three parts: the elastic stiffness matrix ke, the geometric stiffness matrix kʹg, and the bowing matrix k b. The bowing matrix, which considers the influence of member bowing effect and initial out-of-straightness on the beam-column stiffness, is given in Appendix 3. In the beam-column approach, the space element is a direct extension from the planar one, and some coupling terms between the flexural and torsional displacements are lost in the geometric stiffness kʹg. However, these coupling terms have been included in the geometric stiffness matrix kg, which is derived from the virtual work equation by using the stability interpolation functions as given in Sec. 6.2.2.3. Hence, in the nonlinear analysis of frame structures, the geometric matrix kg should be used instead of the matrix kʹg. Although Kondoh and Atluri (1986) considered bowing effect in their beam-column formulation, no allowance has been made for the member initial out-of-straightness. Al-Bermani and Kitipornchai (1990) proposed a deformation matrix to consider the effect of deformed geometry and allow the use of least elements in a nonlinear analysis. However, their formulation has not been tested for space frames in which the member is slender and subject to high axial force. Numerical examples in Liew et al. (2000b) show that the proposed bowing matrix is particularly useful for slender members subjected to high axial force. This method has widened the scope of advanced analysis for many types of space frame structures.

6.2.2.6 Stability and Bowing Functions

16 12 Stability fuctions S1n, S2n

Figures 6.10–6.12 compare the different levels of approximation of the stability functions S1n, S2n, and c0n and the bowing functions b1n, b2n, bvsn, and bvvn. It can be seen from the figures that these parameters vary considerably with the axial force, and thus influence the element stiffness. Chan and Zhou’s expressions (1995) based on the polynomial functions of fifth-order provide good approximation to the accurate values except in the range of high compression load. The advantage of Chan and Zhou’s expressions is that they have no singularity points. However, the exact expressions in Equations 6.15–6.16 and 6.21–6.25 encounter singularity at certain axial load values. To obtain the values at the singularity points of the

8 4

S2n

0 -4

S1n Exact 5th-order (Chan and Zhou, 1995) 3rd-order

-8 -12 -16 -4

-3

-2

-1

0

1

2

3

Normalized axial force P/Pe

FIGURE 6.10 Exact and approximate stability functions S1n and S2n.

4

168


0.10

40

0.09

30

0.07 0.06

b2n

0.05 0.04 0.03

Fuctions c0n, bvsn, bvvn

Bowing fuctions b1n, b2n

0.08

b1n

0.02

Exact 5th-order (Chan and Zhou, 1995) Constant at P/Pe=0

0.01 0.00 -4

-3

-2

-1

0

1

bvvn

20

c0n

10 0 bvsn -10 -20 Exact 5th-order (Chan and Zhou, 1995)

-30

2

3

4

-40 -4

-3


FIGURE 6.11 Exact and approximate bowing functions b1n and b2n.

-2

-1

0

1

2

3

4


FIGURE 6.12 Exact and approximate stability function c0n and bowing functions bvsn and bvvn.

accurate expression, L’Hospital’s Rule will be used and linear approximations adopted for a region near the singularity points. In Chen et al. (1996), stability functions S1n and S2n are approximated by some approximated functions without singularity points. It should be noted that the secant stiffness relationship used by Meek and Loganathan (1989) is a degenerated form of Equation 6.20 by adopting the cubic stability functions S1n and S2n given in Equations 6.17 and 6.18, b1n = 1/40, b2n = 1/24, c0n = bvsn, bvvn = 0.

6.2.2.7 Tangent Stiffness Matrix

The stiffness equation of a beam-column element can be expressed as:

(k

e

+ kg + kb

) du = k

t

du = df

(6.29)

in which du is the incremental displacement vector, df is the incremental force vector, ke is the elastic stiffness matrix, kg is the geometric stiffness matrix based on the stability interpolation functions, k b is the bowing matrix, and kt is the elastic tangent stiffness matrix. It is noted that in the cubic element approach (Orbison, 1982; Yang and Kuo, 1994), the bowing matrix k b is not included, and the geometric stiffness matrix kgc, based on the cubic interpolation functions, are used instead of the matrix kg. In the geometrically nonlinear analysis by using the beam-column element, an improper solution can be found if the joint rotations are represented by the displacement derivatives (Yang and Kuo, 1994). For spatial members, the induced moment matrix k i should be added to the tangent stiffness matrix to make the usual degrees of freedom that are represented by the displacement derivatives in amounts equal to the commutative rotational degree of freedom, and hence to yield the true equilibrium condition and satisfy the rigid body tests. Due to the lack of conjugateness between bending moments and displacement derivatives, k i is asymmetric for a single and discrete element. The symmetry will be restored when the element is connected to other elements. As a result, only the symmetric portion of the induced moment matrix, which is referred to as the joint moment matrix k j, need to be assembled to form the structural tangent stiffness matrix. More detailed research on this issue can be referred to Teh and Clarke (1997, 1999a) and Izzuddin (2002). The induced moment matrix is given by:

k i = Diag[0 3x3 , k ia , 0 3x3 , k ib ]

(6.30)


169

in which:  0 k in =  − M zn   M yn

0 0 0 M xn / 2 − M xn / 2 0

  (n = a, b)  

(6.31)

The joint moment matrix, kj, is given by:

k j = Diag[0 3× 3 , k ja , 0 3×3 , k jb ]

(6.32)

in which:

 − M zn / 2 M yn / 2 0  0 0 k jn =  − M zn / 2  M yn / 2 0 0 

   (n = a, b)  

(6.33)

Liew et al. (2000b) have demonstrated that the use of geometric stiffness kg and induced moment matrix k i enable the prediction of flexural buckling of columns with one element per member, and the prediction of elastic lateral-torsional buckling of beam with rectangular section. By updating the element forces with an additional bowing matrix k b to consider the deformed shape effect together with the natural deformations based on the UL formation, the large-deflection geometrically nonlinear behavior of space frames can be captured with the least element per member. The approach can be naturally extended to the plastic hinge-based inelastic analysis. Hellan (1995) investigated six different initial out-of-straightness patterns on the limit load of jackets using the pushover analyses. The out-of-straightness patterns are prescribed:

1. In the plane of the loading, acting in the direction of each member’s distributed load 2. In the plane of loading, acting in the direction of global base shear 3. According to the (linear) solution vector of the external load 4. According to the elastic system buckling displacement vector 5. According to the displacement vector at system collapse 6. According to the lowest eigenvector of the system stiffness matrix

Hellan (1995) found in a series of numerical analyses that initial out-of-straightness assigned in the direction of each member’s distributed line loads give a more consistent (small standard deviation) and slightly more conservative capacity prediction than do the other patterns investigated. Other patterns give more scatter in results and, in a number of cases, produce results where the presence of initial out-of-straightness leads to an increase in estimated collapse capacity compared with results for the initially straight structure. In the past few decades, there has been a debate regarding the merits of the cubic element vis-à-vis the stability function-based beam-column for steel frame analysis (Teh, 2001; Teh et al., 2001; Chan and Gu, 2001). Teh (2001) demonstrated that in the practical analysis and design of steel frames, cubic element approach is sufficient to capture the elastic buckling and large-displacement behavior. However, his cubic beam element approach adopts the secant stiffness relationship to update the element forces, which is difficult to extend to the plastichinge analysis that is based on force and displacement increments. As pointed out by Chan and Gu (2001), the stability function-based element—while considering the bowing effect and initial out-of-straightness—enables the advanced analysis established on a more accurate and powerful foundation.

170


6.2.3 Modeling of Material Nonlinearity in Beam-column 6.2.3.1 Methods for Modeling Material Nonlinearity

Material nonlinearity in the form of cross-sectional plastification and spread of yielding along member length can be modeled by employing the finite element-based inelastic analysis methods or various numerical approaches that can be found in Chen and Atsuta (1976, 1977). Since the finite element method is the most versatile method for structural analysis, it is widely used in the inelastic analysis of frame structures. In general, these finite element-based inelastic models can be categorized into five main types, as covered in the next five sections. 6.2.3.1.1 Distributed Plasticity Analysis This method is also called spread-of-plasticity analysis or elasto-plastic analysis. Distributed plasticity analysis such as the plastic zone analysis (White, 1986; Clarke, 1994; Pi and Trahair, 1994; Teh and Clarke, 1999b; Jiang et al., 2002) and 3-D shell element inelastic analysis (Avery and Mahendra, 2000a) involves explicit modeling of the gradual yielding in the volume of the structure through discretizing members along length and through cross-sections. It can model the residual stresses, geometric imperfections, material strain hardening, and elastic unloading. If correctly formulated to include all significant behavioral effects, it is considered to provide an analytically exact structural solution and can be classified as an advanced analysis technique in which design specification checks for the member and section capacities are not required. However, distributed plasticity analysis is usually computationally intensive with the increase of structural size. The cost and effort of such methods are often so great that analyzing complete medium-to-large structures is often prohibitive. Therefore, this method is normally used to check and calibrate the accuracy of simplified inelastic analysis methods and to establish design charts and equations. One potential application of distributed plasticity analysis is to adopt the mixed element techniques in which the analysis might use coarser element discretization with plastichinge based procedures where these computational models suffice, and spread-of-plasticity approaches where more rigorous models are required to capture the performance (Jiang et al., 2002; Liew and Chen, 2004a and 2004b). 6.2.3.1.2 Plastic-hinge Analysis The plastic-hinge analysis is also called the concentrated plastic-hinge analysis or elastic-plastichinge analysis. It can be traced to earlier works using a single plastic strength surface by Nigam (1970) and Porter and Powell (1971). Refinements to the method have been made in the process of implementing it for the inelastic analysis and design of transmission towers (Al-Bermani and Kitipornchai, 1990 and 1992; Kitipornchai and Al-Bermani, 1992), and frame and tubular structures (Orbison et al., 1982; Creus et al., 1984; Ueda et al., 1985; Bozzo and Gambarrotta, 1985; Wong and Tin-Loi, 1987; Ziemian et al., 1992; Chen and Toma, 1994; Papadrakakis and Papadopoulos, 1995; Chen et al., 1996; Krenk et al., 1999; Liew et al., 2000b). Plasticity is formulated based on the cross-sectional stress-resultant constitutive model, which represents the plastic interaction between axial force and biaxial moments. If the forces at any particular cross-section reach the plastic strength capacity, the cross-section changes abruptly from an elastic to fully plastic state, and a plastic hinge forms. The plastic-hinge analysis normally employs one beamcolumn element per member and is computationally more efficient and economical than the distributed plasticity analysis. For slender structure in which elastic instability is the predominant mode of failure, both the plastic-hinge analysis and the distributed plasticity methods lead to almost identical results. For structures that exhibit significant yielding in the members, or when structural behavior is dominated by the instability of a few members, the plastic-hinge analysis often over-predicts the actual


171

stiffness and strength of the structure. Due to the simplifying approximations inherent in the plastic-hinge analysis, it is generally not accurate enough to be classified as an advanced analysis. Therefore, some refinements to the basic plastic-hinge theory are necessary to generalize its application for the analysis of any structural system. 6.2.3.1.3 Modifications to Plastic-hinge Analysis A significant quantity of research works have been done to propose modification to the plastichinge analysis to consider the degradation of stiffness due to the spread of plasticity. These alternative approaches are comparable to the plastic-hinge analysis in efficiency and simplicity, but provide results of accuracy comparable to the distributed plasticity solutions. These models include hardening plastic-hinge analysis (King et al., 1992), refined plastic-hinge analysis (Liew et al., 1993a), the notional load plastic-hinge analysis (Liew et al., 1994), quasi plastic-hinge analysis (Attalla et al., 1994) and improved quasi plastic-hinge analysis (Leu and Tsou, 2001; Leu et al., 2008), modified tangent modulus approach (Ziemian and McGuire, 2002), and two-surface plastic-hinge analysis (Himly and Abel, 1985; Powell and Chen, 1986; Deierlein et al., 1991; Hellan, 1995; Al-Bermani et al., 1995; Liew et al, 1998; El-Tawil and Deierlein, 1998; Krenk et al., 1999; Liew and Tang, 2000; Skallerud and Amdahl, 2002; Hajjar, 2003; Ma and Liew, 2004). The notional load plastic-hinge analysis applies the notional lateral load of 0.5 percent of the story gravity loads to account for the effects of distributed plasticity and structural imperfection caused by residual stresses and initial member out-of-straightness and frame out-of-plumbness. The advantage of this method is that there is no need to modify the base plastic-hinge analysis. Refined plastic-hinge analysis considers the effect of gradual yielding, residual stresses, and geometric imperfections by using the tangent modulus and reduction functions for flexural stiffness. Both analysis methods have been verified by using many well-established calibration frames that range from simple beam-columns to braced and unbraced frames, from theoretical to experimental frames, and from plasticity-dominated to stability-dominated cases. They have been recommended for practical advanced analysis of steel plane frames composed of members with compact sections that are fully braced out-of-plane (Chen and Toma, 1994; Chen et al., 1996; Liew et al., 1997b). The hardening plastic-hinge analysis degrades the member stiffness in a way similar to that of the refined plastic-hinge analysis. Quasi plastic-hinge analysis uses the inelastic stiffness matrix to consider the gradual plastification under combined action of bending moment and axial force. Attempts have been made by Attalla et al. (1996) for extending the quasi plastic-hinge analysis for the inelastic nonuniform torsion analysis. The modified tangent modulus approach adopts a relatively simple expression to reduce the modulus of elasticity of individual elements according to the amount of axial force and minor-axis bending moment. The two-surface plastic-hinge analysis extends the plastic-hinge method and allows for the gradual plastification effect by employing the yield surface and bounding surface in force space (Liew and Tang, 2000). 6.2.3.1.4 Flexibility-based Inelastic Analysis Many of the nonlinear formulations presented in the literature are based on the stiffness or displacement method for its relative ease in implementation when compared with the flexibility or force method. The stress resultants obtained by a displacement-based model generally do not satisfy the governing differential equation of equilibrium for the inelastic member. Equilibrium is satisfied only in a variational sense. The assumed displacement interpolation may over-constraint the element in an inelastic state. If the element formulation is based on the interpolation of forces, then a model can be established in which the equilibrium, compatibility, and constitutive conditions are satisfied exactly. This type of model is referred to as an equilibrium-based or a flexibilitybased element (Taucer et al., 1991). This method has been extended for the inelastic analysis of frame structures by Nukala and White (2004) and Alemdar and White (2005).

172


6.2.3.1.5 Mixed Elements Approach Jiang et al. (2002) and Liew and Chen (2004) proposed a mixed-element approach that allows for adapting the refinement of the structural model to the expected response. In this approach, the structure model consists of different zones where the members may have different levels of discretization (Figure 6.13). A more refined modeling is adopted at critical zones where the members would exhibit significant inelastic and stability effects. Global analysis may be carried out on the structure primarily modeled by beam-column elements, whereas localized buckling effects may be modeled by the spread-of-plasticity fiber elements. The mixed element model is made possible by enforcing force and displacement compatibility at the connecting nodes of the members (Chen and Liew, 2005). The spread-of-plasticity elements and the plastic-hinge beam-column elements can coexist within the same model as illustrated in Figure 6.13. This approach has found great potential for analyzing large-scale 3-D framework subject to blast and fire attack (Liew, 2008).

6.2.3.2 Plastic Strength Surface

In theory, it is possible to develop exact expressions of cross-sectional plastic criteria (see Chen and Atsuta, 1976). However, most plastic-hinge methods rely on a simplified force interaction expression to approximate the plastic strength surface. For 2-D analysis, either piecewise linear or continuous functions are commonly used. For 3-D analysis, continuous functions are usually preferred over the multifaceted surfaces. Single-equation plastic surfaces for solid rectangular and circular sections and circular hollow section have been theoretically derived in Duan and Chen (1990). Exact interaction formulas for box-type cross-sections are difficult to obtain. Instead, approximate expressions are derived numerically in Duan and Chen (1990). Single-equation plastic strength surfaces for channel, tee, and angle sections have been proposed by Al-Bermani and Kitipornchai (1990) and Kitipornchai et al. (1991), which were applied for the nonlinear analysis of transmission towers (Al-Bermani and Kitipornchai, 1992). Single-equation plastic strength surfaces for compact wide-flange sections have been proposed by Orbison et al. (1982), Duan and Chen (1990), and Attalla et al. (1994). The three plastic strength surfaces are interaction functions of a member’s axial force and biaxial bending moments. They are symmetric about the three coordinate planes. Duan and Chen’s, as well as Attalla’s, plastic strength surfaces are more accurate than Orbison’s plastic strength surface. However,

P

P

H Torsional-flexural buckling Local buckling slender section

FIGURE 6.13 Use of mixed elements for inelastic analysis.

Compact Section


173

they have sharp vertices at the limits of pure axial force or at pure moment where the normal of the plastic strength surface cannot be uniquely defined. Numerical difficulties may arise when the force point of a plastic hinge crosses these vertices. An iteration scaling procedure proposed by Izzuddin and Elnashai (1993a) may be adopted to bring the force state back to the plastic strength surface. In the case of pure axial plasticity, a simple procedure to overcome such problems associated with shape vertice. Orbison’s plastic strength surface has full slope continuity that eliminates the numerical difficulties associated with vertices. With the exception of the heavy wide-flange sections subject to the combined effect of the weak-axis bending moment and axial force, it gives a good prediction on the plastic strength of the light- to medium-weight wide-flange sections. In the offshore industry, plastic strength surfaces for various shapes of chord section in the jackup leg structure (such as tubular chords with double central racks, split tubular chords with double central racks, triangular chords with single racks, etc.) have been proposed in SNAME (1994) and Marshall et al. (2001). For frame structures, plastic-hinge analysis is usually based on a plastic criterion that considers the longitudinal normal stresses due to axial force and bending moments, often neglecting shear stresses due to shear force, torsion, and bimoments. By treating an I-section as a composition of three thin plates, the plastic strength surface diagrams have been established by Yang and Fan (1988) and Yang et al. (1989) for I-sections subjected to the axial force, two bending moments, torque, and bimoment. Based on an optimization formulation, Osterrieder and Kretzschmar (2006) developed a general approach to evaluate the plastic steel section capacity for any type of open thin-walled steel sections and any combination of internal forces.

6.2.3.3 Concentrated Plastic-hinge Formulation

Plastic hinges are introduced when the element end forces reach the plastic strength surface. Associated flow rule assumes that the state of forces at a plastic hinge keeps moving on the plastic strength surface and the incremental plastic displacement vector is normal to the plastic strength as shown in Figure 6.14. Φ = 0 represents the full plastification of the cross-section, and Φ = −1 is the value of a stress-free cross-section. In principle, a state of forces characterized by Φ > 0 is illegal. P

One octant of plastic strength surface, Φ Incremental forces Incremental plastic deformations

Mz

My FIGURE 6.14 Cross-sectional force behavior at plastic hinge.

174


The flow rule for an element with plastic hinges formed at both ends is expressed as: 0 gb

 g du p =  a  0

  ∆λ a     ∆λ b

  = G ∆λ 

(6.34)

in which dup is the incremental plastic displacement vector, Δλi (i = a, b) is the plastic scalar, and gi is the normal of plastic strength surface given by: T

∂Φ ∂Φ ∂Φ  ∂Φ  ∂Φ ∂Φ ∂Φ (6.35)  gi = = ∂fi  ∂Fx ∂Fy ∂Fz ∂M x ∂M y ∂M z    in which fi is the force vector at element end. The element incremental displacement vector is separated into an elastic component and a plastic component: du = du e + du p

(6.36)

The stiffness equation can be obtained by introducing the flow rule from Equation 6.34:

)

(

df = k t du − du p = k t du − k t G ∆λ

(6.37)

For a perfectly plastic hinge, the plastic strength surface is fixed, and df must always be tangent to the surface, hence: G T df = G T k t du − G T k t G∆λ = 0

and the vector of plastic scalars can be solved as:

(

)

∆λ = G T k t G

−1

G T k t du

(6.38) (6.39)

Substituting Δλ into Equation 6.37, the elastic-plastic stiffness equation is obtained:

(

)

(

df = k t + k p du = [k t − k t G G T k t G

in which kp is the plastic reduction matrix and k

EP t

)

−1

G T k t ] du = k EP du t

(6.40)

is the elastic-plastic tangent stiffness matrix.

6.2.3.4 Two-surface Plastic-hinge Formulation

A plasticity model that accounts for partial yielding and hardening employs two interaction surfaces—one yield surface and one bounding surface—as shown in Figure 6.15 (Liew and Tang, 2000; Ma and Liew, 2004). The bounding surδ face encompasses the cross-sectional force state S2 g and the yield surface at any stage during the Bounding g yielding process. To keep the two surfaces from surface, Φb overlapping during translation, the initial yield S surface is assumed to be a scaled-down version β S of the bounding surface. In reality, the initial yield surface and the α Yield surface, Φy bounding surface are different in shape. Major deviation occurs in axial loading. Adoption of the same shape for the first yield and fully plastic surfaces would under-predict the axial stiffness. This may be remedied by tuning the S1 hardening parameters that describe axial hardening by values other than those for the pure FIGURE 6.15 Schematic of initial yield surface bending case, and then a steeper transition be- and bounding surface.


175

tween the axial yield and full plasticity can be obtained (Skallerud and Amdahl, 2002). A study by El-Tawil and Deierlein (1998) shows that the simplified results are satisfactory for bisymmetrical sections under biaxial bending and under a combination of axial load and major-axis bending, but may not be as good for sections under a combination of axial load and minor-axis bending. When the force state S remains within the initial yield surface, the member is elastic and there is no translation of the two surfaces. Once the force state S has reached the initial yield surface, the inner surface starts to translate so that the stress resultants remain on the yield surface during subsequent loading. This translation is uniquely defined by the history of the position vector β, which marks the center of the yield surface. Translation of the bounding surface is at a much slower speed and is controlled by the kinematic hardening rule and defined by the history of center position vector α. To prevent the yield and bounding surface from intersecting during translation, Mroz’s conjugate point approach is adopted to describe translation of the initial yield surface. For a given force state S that has reached the yield surface, a conjugate point S on the bounding surface is defined so that S and S have equal g and g gradients. The yield surface translates parallel to the vector that connects the current force point and the conjugate point on the bounding surface. In the two-surface model, the plastic hardening parameter and transition parameter are specific to each force component, and they may be determined by calibration with tests or more exact solutions. Numerical calibration work has been carried out by Punniyakotty (1998) to determine the appropriate parameters to predict the capacity of steel members. Liew and Tang (2000) investigated the effect of member imperfections and calibrated the inelastic beam-column model for advanced analysis of tubular structures.

6.2.3.5 Numerical Strategies for Plastic-hinge Analysis

6.2.3.5.1 Elastic Unloading at Plastic Hinge The plastic scalar Δλ defined in Equation 6.39, which characterizes the plastic displacement magnitude, is zero for an elastic state and positive for a plastic state. When a plastic hinge occurs at the cross-section, the value of the plastic scalar changes from zero to a positive value. When elastic unloading occurs at the plastic hinge, it changes from a positive value to a negative one. Then its actual value has no meaning and only its negativity indicates that elastic unloading occurs. If elastic unloading is detected, the structure is re-analyzed within the same load step after modifying the stiffness matrices of elements in which elastic unloading occurs. 6.2.3.5.2 Pure Axial Plasticity Plastic hinges may form at both ends of the strut due to the action of pure axial force. These may be the cases when analyzing trusses and braced frames involving pin-ended members. Numerical difficulty may be encountered in calculating the plastic reduction matrix because the axial plastic deformations are of arbitrary magnitude at both ends of element, and the matrix GT k tG, which appears in the plastic reduction matrix, is singular and cannot be inverted. In the present work, a simple technique has been developed to overcome this problem. Each element, with plastic hinges forming at both ends, is checked for the presence of bending moments prior to the calculation of the elastic-plastic tangent stiffness matrix. If the element is found to be in a plastic state due to pure compression or tension, the elastic-plastic tangent stiffness matrix is computed as the elastic tangent stiffness matrix, and the terms associated with axial stiffness are then removed. This method can capture the plastic behavior of element correctly with minimum computational effort. 6.2.3.5.3 Plastic Hinges at Common Node Adjoining Two Elements Plastic hinges may occur simultaneously at a common node adjoining two elements. In this case, the rotational stiffness at the node will become very small. The severely ill conditioned stiff-

176


ness matrix will result in large incorrect displacements of that node. The element formed with a common plastic hinge can be modeled using two parallel elements: a plastic-hinge element and an element that is always elastic and has a small elastic modulus to simulate strain hardening. The element tangent stiffness matrix is obtained by adding the stiffness matrices of the two parallel elements together. This model ensures a finite stiffness when all elements at a common node have formed plastic hinges. To reduce the unnecessary computational expense, this model is used only for the elements that have formed a plastic hinge. 6.2.3.5.4 Formation of Plastic Hinge Within the Member Length A plastic hinge may sometimes form within the member length. A tedious and approximate procedure is to model each frame member with several elements. However, this method will increase the overall degrees of freedom of the structure, and becomes computationally expensive. Moreover, in most cases, only a few members in a structure will have plastic hinges forming between the member ends. Abdel-Ghaffar et al. (1991) developed a formulation that can model the plastic hinge forming at any location within the beam, which is under the uniformly distributed load as well as multiple concentrated loads on the member. Chan and Zhou (2004) proposed a method for plane steel frame in which plastic hinges are allowed to form in an element with two at the two ends and one at the location of maximum combined stress due to axial force and moment. An efficient method for modeling the plastic hinge within the member length in space steel frames is to use the static condensation method with minimum computational effort as shown in Figure 6.16. Based on the member initial out-of-straightness, the deformed member shape, and the forces at member ends, the force state within the member length can be established by taking the equilibrium of axial force and moment at the internal cross-section. It is strictly not necessary to compute the exact location of the plastic hinge for an accurate estimate of member strength. As long as the exact location of the plastic hinge in a member is not more than a distance L/5 (L = member length) away from the assumed position, the difference in strength prediction is

M2 > M1

M1

P

P

M2

L

M

M2

M1 x

M(x) =

(M1 cos kL + M2) sin kx − M1 cos kx sin kL

FIGURE 6.16 Formation of plastic hinge within the member length.

x

kL = PL2/EI


177

no more than 5 percent (Chen et al., 1996). The element length is divided into six segments with equal length. The cross-sectional forces are then checked at five points between the member ends. A plastic hinge is said to have formed when the plastic strength is reached at any of these points. The analysis will automatically subdivide the original element into two subelements at the plastic hinge location as shown in Figure 6.16. The internal hinge is then modeled by an end hinge at one of the subelements. The stiffness matrices for the two subelements are determined. The inelastic stiffness properties for the original element are obtained by static condensation of the extra node at the location of the internal plastic hinge. Since the static condensation process is only performed at the element level, it does not involve much computational cost. 6.2.3.5.5 Load Increment Control If a plastic hinge occurs, the load increment is scaled so that the element forces of that crosssection comply exactly with the plastic strength surface. This is indicated in Figure 6.17, which is a 2-D projection of the 3-D plastic strength surface. At the beginning of a load step, the state of a cross-section at Force Point A is elastic. However, at the end of the load step, the force state reaches Point B. A simple check of the plastic strength surface shows that a plastic hinge has formed during the load step. Consequently, the load increment is scaled down to find Force Point C, which lies on the plastic strength surface. The scaling factor γ is determined by the bisection method. Figure 6.18 shows that Force Point A lying on the plastic strength surface may have deviated excessively to Force Point B. The load increment is reduced to find Force Point C, which lies on the surface Φ = ε2. The tolerance for overshooting the plastic strength surface is selected as ε2 = 0.005. The scaling factor γ is also determined by the bisection method. The final load increment is the minimum value determined by using the above constraints. After the load increment is completed, the nodal coordinates, element forces, and geometry are updated. Then it is checked to see if new plastic hinges have formed. In some cases, plastic hinges may occur at approximately the same applied load level, resulting in a series of small load increments. In order to avoid small load increment in case of frequent occurrences of plastic hinges, an incipient plasticity tolerance ε1 = 0.005 can been implemented. Once the force point at a cross-section locates outside the surface Φ = −ε1, a plastic hinge is inserted. In this way, exact scaling to the plastic strength surface is not always possible and several plastic hinges may be inserted during one load increment. p = P/Py

p = P/Py dm γ dm

γ dm

B

C A

dm

γ dp

dp

C

A D

Plastic strength surface, φ = 0 m = M/Mp

FIGURE 6.17 Load increment scaled back to the plastic strength surface.

Plastic strength surface, φ = 0

B

γ dp

dp

surface, φ = ε2

m = M/Mp

FIGURE 6.18 Load increment scaled down by the constraint of force increments at plastic hinge.

178


6.2.3.5.6 Control of Deviation of Yield Surface When a plastic hinge forms at a cross-section, the force point is constrained by a plastic reduction matrix to move tangentially on the plastic strength surface. A drift of the force point from the plastic strength is inevitable. Various methods have been proposed to rectify the nonconformity of the plasticity condition. Hodge (1977) devised a technique to confine the force point movement to an area bounded between two yield surfaces, a procedure that Bozzo and Gambarotta (1985) later extended to include geometrical nonlinearity. Wong and Tin Loi (1987) proposed the piecewise linearization of the convex nonlinear plastic strength surface, thereby guaranteeing the satisfaction of both equilibrium and plasticity condition. Orbison et al. (1982) used a multistep iterative predictor-corrector-type procedure to force the force point back onto the plastic strength surface. Ma and Liew (2004) corrected the deviation from the plastic surface by applying an equivalent nodal load at element ends to regain plastic strength surface agreement in the succeeding increment. This method can be consistently extended for the inelastic analysis of steel frames under fire in which the plastic strength surface may contract due to the temperature effect.

6.2.3.6 Plasticity Formulation at Elevated Temperature

The thermal effects on the structural elements may be considered by conducting heat transfer analysis. The temperature history in each structural member is first calculated based on the fire model assumed. The equivalent nodal expansion forces for the line element are evaluated based on the incremental temperature change. The thermal effects on the structural element include the reduction of yield stress and elastic modulus, and thermal expansion at elevated temperatures. Consistent nodal forces are produced on an elastic element at elevated temperatures due to the axial expansion and temperature gradient increment over the cross-section. Landesmann et al. (2005) extended the second-order refined plastic-hinge analysis proposed by Liew et al. (1993a) for plane steel-framed structures under fire conditions. Chan and Chan (2001) developed the plastic-hinge analysis of steel frames based on the spring-in-series model considering the combined effects of sectional plasticity and connection flexibility. Liew et al. (1998), Ma and Liew (2004), and Liew (2004b) extended the two-surface plastic-hinge model to model the behavior of 3-D steel frames under fire. At elevated temperatures, the reduction of yield strength causes degradation of the cross-section capacity. The yield and bounding surfaces thus have to be reduced in order to satisfy the yield condition. Degradation of the yield strength is based on the effective strength concept. At high temperatures, the stress-strain relationship of steel is highly nonlinear and does not exhibit a distinct yield plateau. The idea of effective yield strength is introduced to define a yield plateau at a relatively high level of strain. For the two-surface plasticity model, the size of the bounding surface that corresponds to full cross-sectional plasticity follows the reduction curve for effective yield strength in Eurocode 3, Section 3.2 (CEN, 2001). The size of the initial yield surface is given by the temperature-invariant scaling factor zy. At ambient temperature, zy is usually taken as the reciprocal of the shape factor, and can be reduced further to account for the initial residual stress effect. At elevated temperatures, the initial yield surface is assumed to degrade proportionally to the bounding surface as shown in Figure 6.19. However, the initial yield strength decreases at a faster rate than the effective yield strength; therefore, the size of the initial yield surface is over-predicted at higher temperatures if a constant zy value is adopted. In practice, this will not have any significant effect on the inelastic behavior of members on fire. For a more accurate prediction, the zy parameter can be adjusted to a lower value by calibrating the size parameter close to the critical temperature. After a yield hinge forms, the yield surface continues to contract with an increase in temperature (Figure 6.19). This will cause the resultant stress to leave the yield surface. This effect can be accounted for by including an additional term that represents the change of yield surface due to the temperature increment. The change of yield stress is considered to contribute to the increment


179

P/Py 1.0

Bounding surface at ambient temperature

P = Py0

Constricted surface at temperature t0 σij-1 1.0

Mz/Mpz

Mz = Mz0

My = My0 1.0 My/Mpy

FIGURE 6.19 Constricting bounding surface at elevated temperatures.

of consistent nodal forces, which is required to make the force state remain on the contracting yield surface. Verification of the two-surface plasticity model at ambient and elevated temperatures for both components and frames over a wide range of parameters was reported by Liew et al. (1998) and Ma and Liew (2004).

6.2.3.7 Modeling of Lateral-torsion Buckling

As pointed out by White et al. (2006), although some progress has been made on 3-D distributed plasticity methods considering the nonuniform torsion (Pi and Trahair. 1994; Izzudin and Smith, 1996; Nukala and White, 2004), the complexity and cost of the analysis is significantly greater due to the appropriate handling of residual stresses, geometric imperfections, warping continuity at beam-to-column joints, local-overall member buckling interactions, and restraint from and interaction with floor slabs. Other important attributes that can influence the 3-D response have not been studied thoroughly at this time. A practical advanced analysis for planar steel frame design with consideration of out-of-plane buckling has been proposed by Wongkaew and Chen (2002) and Trahair and Chan (2003). The analysis can be simplified by separating it into two stages. First, an in-plane advanced plastic-hinge analysis is carried out to check whether the structure can resist the loads by in-plane behavior. If it cannot, the structure is inadequate and must be modified. If it can, the second stage outof-plane buckling analysis would be carried out to check whether the structure has sufficient out-of-plane resistance. If it does not, the structure is inadequate and must be modified. If it does, the structure is adequate. The moment and axial force distributions found from in-plane analysis can be used directly in the out-of-plane analysis.

6.2.3.8 Modeling of Local Buckling

In the advanced analysis, a ductility check must be performed to ensure that beam-columns have adequate inelastic rotation to develop their full-plastic moment capacity. In most cases, local instability is forestalled if cross-sections are made compact because compact sections are capable of

180


developing the full-plastic moment capacity and sustaining large hinge rotation before the onset of local buckling. For steel frames composed of wide flange sections, Ziemian et al. (1992) proposed that two checks carried out to ensure that adequate ductility is provided at the hinged cross sections. The first check compares the required major axis inelastic rotation angles with the theoretical angular rotation capacity of the sections. The second check compares the required major axis inelastic rotation capacities with the available rotation capacities. In the analysis of a 22-story office building frame, Ziemian et al. (1992) found that a majority of the hinged cross sections had inelastic rotation demands in less than 50 percent of the theoretical rotation capacities. Recently, Van Long and Hung (2008) developed the local buckling check according to Section 5.3 of Eurocode 3 for plastic-hinge analysis of 3-D steel frames with I-shaped sections. For fabricated circular hollow sections, simple critical strain criteria based on the outside diameter over wall thickness (D/t) ratio have been proposed based on the experimental results (Sohal and Chen 1988; Skallerud and Amdahl, 2002). To assess possible local failure modes such as local buckling and fracture, estimates of the plastic straining are required. Unfortunately, the plastic-hinge concept assumes zero hinge extension, and therefore implies infinite strains and is unable to provide the correct information of the strains within member length. Based on some engineering mechanics assumption, Moan et al. (1991) developed a procedure to predict the local strain of beam-column within the plastic-hinge framework. Noncompact sections are often used in steel frames with cold-formed sections to achieve both construction economy and structural efficiency. For such frames, local buckling may occur before the structure reaches its maximum capacity. Avery and Mahendran (2000b) modified the refined plastic-hinge analysis (Liew et al., 1993a) to account for the effect of local buckling using simple equations derived from the codes. In the offshore industry, in addition to normal functional and environmental loads, accidental loads due to collision, falling objects, blast, and fire, etc., might occur. The extent of damage caused by these loads ranges from the possibility of total structural collapse to small damages on structural components. Such damages may not have serious consequences at the time of accident, but may later affect the ability of the structure to resist loads. Taby and Moan (1985) and Søreide et al. (1994) investigated the ultimate strength and post-buckling behavior of circular and rectangular hollow steel tubes containing dent damage, which are useful for making optimal design decisions regarding safety and economy.

6.2.4 Updating of Element Forces and Geometry in Beam-column

An important phase in the nonlinear analysis is to update the element geometry and forces based on the displacement increments obtained in the solution phase. By summing the element forces at each node and comparing them with the external loads, the structural unbalanced forces can be computed and iteration is repeated until equilibrium is achieved. In their nonlinear geometric analyses of plane frames, Yang and Leu (1994) concluded that the accuracy of the numerical solutions depends primarily on the corrector or procedure for recovering the element forces.

6.2.4.1 Force Recovery Based on the Natural Deformation Approach

In the beam-column approach (Oran, 1973; Kassimali and Abbasnia, 1991; Chan and Gu, 2000), the member forces are updated using the secant stiffness that relates them to the member basic deformations. In contrast, the finite element approach based on the updated Lagrangian formulation leads to the tangent stiffness, which relates the incremental element forces to the incremental element displacements. Element forces can be rationally recovered by employing the direct approach, the external stiffness approach (Yang and Kuo, 1994), and the natural deformation approach (Gattass and Abel, 1987b; Yang and Kuo, 1994).


181

The direct approach calculates the incremental element forces referred to the previous configuration from the incremental element displacements by using the tangent stiffness matrix. Since it does not account for the effect of rigid-body rotation in the large displacement problems, it is often necessary to specify a sufficient number of load increments to ensure that the incremental displacements are reasonably small. In the external stiffness approach, the external stiffness terms associated with rigid-body rotation are isolated from the tangent elastic stiffness matrix so that the remaining stiffness matrix can be used to obtain the force increments referred to the current configuration. However, the external stiffness approach cannot be employed in the plastic-hinge analysis because it is difficult to isolate the terms associated with rigid-body rotation from the tangent elastic-plastic stiffness matrix. In the natural deformation approach, the incremental element displacements can be conceptually decomposed into two parts: the rigid-body displacements and the natural deformations. The rigid-body displacements serve to rotate the initial forces acting on the element from the previous configuration to the current configuration. The natural deformations constitute the only source for generating the incremental forces. Based on the plastic-flow rule, the force point at the plastic hinge will move on the plastic strength surface. The natural deformation approach is adopted due to its consistence with the plastic-hinge analysis and its accuracy in updating the incremental element forces. An efficient formulation proposed by Conci (1992) may be used to calculate the natural deformations for the nonlinear analysis of frameworks. The element incremental displacements between configurations C1 and C2, can be conceptually decomposed into two parts: the rigid-body displacements dur and the natural deformations dun. The basic idea in calculating the natural deformations is to define a configuration C2ʹ if the element at C2 is translated by -ua, -va and -wa along the 1x, 1y, and 1z axes so that there are no rigid-body translations between C1 and C2ʹ (see Figure 6.20). The rigid-body rotations are given by (Conci, 1992): 1 (θ + θ xb 2 xa

φx =

φ y = − arctan 1

φz = arctan 1

)

(6.41)

wb − wa

(6.42)

L + ub − ua vb − va

(6.43)

L + ub − ua

in which the rigid-body axial rotation is taken as the average of the axial rotations at element ends A and B. 1y

φy

1

a = 2a φz

1

z

1L

C1

ub − ua 1

C2' 2L

2

vb − va

FIGURE 6.20 Rigid-body rotations.

b

b

wb − wa

1x

182


The element natural deformations are calculated as: T

(6.44) du n =  0 0 0 α xa α ya α za ∆ x 0 0 α xb α yb α zb  in which αxa = θxa − ϕx, αya = θya − ϕy, αza = θza − ϕz, Δx = 2L − 1L, αxb = θxb − ϕx, αyb = θyb − ϕy, αzb = θzb − ϕz, and 1L and 2L are the length of the element at configurations C1 and C2, respectively. These natural flexural deformations are illustrated in Figure 6.21. The effect of rigid-body translations and rotations is to rotate the initial forces acting on the element at C1 as the forces acting on the element at C2 and referred to the axes of C2. The result is the preservation of equilibrium of the element in the displaced configuration with no change on the magnitudes of the element forces at C1. The incremental forces generated by the natural deformations dun, during the incremental step can be calculated as ktdun. By adding it to the initial element forces 11 f at configuration C1, the total element forces 22 f at configuration C2 and referred to C2, can be obtained as:

2 2

k t du n f = 11 f +

(6.45)

6.2.4.2 Geometry Updating and Web-plane Vector

In nature, large spatial rotations are not commutative so that the geometry updating procedure for spatial frames is not a simple extension of that for planar frames. Oran (1973) and Kassimali and Abbasnia (1991) proposed the joint orientation approach, which employs the joint orientation matrices and the member orientation matrices to update the element configurations. Based on 1

y

1

αza 1

a = 2a

L + ub − ua

θza

φz

a = 2a

θya

αyb 1

1

b vb − va

1

b

1

x

1

b

1

x

L

αya

−φy

2

αzb

θzb 1

1

φz

L + ub − ua

wb − wa

−φy θyb

2

z

FIGURE 6.21 Calculation of natural deformations.

b


183

the joint orientation approach, Kuo et al. y (1993) proposed a method to update the element configurations and calculate the natural deformation suitable for use in the z a updated Lagrangian formulation. Izzuddin and Elnashai (1993b) adopted a pair of end-section orientation matrices for each element and reduced the storage and computational effects of a pair of joint orientayˆ tion matrices, the undeformed orientation Unit web plane vector matrix, and the current orientation matrix b for each element in the method proposed zˆ x by Kuo et al. (1993). a The web-plane vector approach proposed by Orbison (1982) is adopted due to its highly computational efficiency and FIGURE 6.22 Web-plane vector of element. straightforward numerical implementation. In this approach, each element is assigned with a web-plane vector (located at the element end A) that lies along the positive local y-axis and is perpendicular to the longitudinal axis of element shown in Figure 6.22. The updating of the web-plane vector is simplified by assuming that the element is straight at the start of each increment and does not develop plastic torsional deformations. However, if a long and torsionally flexible member is expected to undergo large elastic torsional rotations, it is recommended that the member be subdivided into a series of shorter elements. In updating the web-plane vector, the six element rigid-body motions need to be considered. It is clear that the three rigid-body translations have no effect on the components of web-plane vector, and only the three rigidbody rotations change the web-plane vector. The rigid-body rotation about the element’s longitudinal axis ϕx, as given by Equation 6.41, will alter the web-plane vector. In Figure 6.23, the element is observed in the negative local 1x axis at configuration C1. The web-plane vector at the start of the increment is identified as 1 yˆ . After the axial rotation, the web-plane vector is partially updated as: 1

)

yˆ ′ = ( cos φ x 1 yˆ + ( sin φ x

)

1

zˆ

(6.46)

The two remaining rigid-body rotations—one about the element 1y axis and the other about the element 1z axis—are considered next. A rotation about the 1y axis has no effect on the components of the web-plane vector. Although a rotation about the 1z axis will alter the partially updated webplane vector, it will remain in the updated 2x-2y plane. The unit beam vector at configuration C2 can be computed straightforward as: 2

 xˆ =  

2

Xb − 2 Xa 2

L

Yb − 2Ya 2 L

2

2

Zb − 2 Za   2 L 

T

(6.47)

in which 2Xi, 2Yi, and 2Zi (i = a, b) are the updated global nodal coordinates obtained by adding the accumulated nodal translations to their respective coordinates. A third vector perpendicular to the beam vector and the partially updated web-plane vector is created by the cross product: 2

z = 2 xˆ × 1 yˆ ′

(6.48)

As xˆ will typically not be perpendicular to 1 yˆ ′ , vector z will not be a unit vector and its components must be scaled back to generate the unit vector 2 zˆ . 2

2

184


1ˆ

y'

1ˆ

y'

φx

a

2ˆ

y

(cos φx)1yˆ 2ˆ

z

1ˆ

(sin φx) z

2ˆ

x

b

FIGURE 6.23 Updating of element local coordinate: (a) partially updated web-plane vector 1 yˆ ′ ; (b) construction of unit vectors 2 yˆ and 2 zˆ .

In the final step, the fully updated unit web-plane vector is produced by the cross product:

2

yˆ =

2

zˆ ×

2

xˆ

(6.49)

The local coordinate at configuration C2 can be updated based on the updated unit beam vector, the unit web-plane vector, and the unit third vector. For the beam-column element with twelve degrees of freedom, the element local-to-global transformation matrix is given by:

Γ = Diag  γ γ γ γ 

(6.50)

in which γ is the rotation matrix given by:  cos α x cos β x cos δ x β y cos δ y  (6.51) γ =  cos α y cos    cos α z cos β z cos δ z     axis and each of the global X, where α, β, and δ designate the angles between the subscriptal local Y, and Z axes. The element stiffness matrix in the global coordinate K can be obtained by transforming the element stiffness matrix in the local coordinate k as:

K = Γ T k Γ

6.2.5 Modeling of Truss Element

(6.52)

Murtha-Smith (1994) presented the chronological development of various analytical strut models and highlighted the limitation of their use in actual design practice. Blandford (1997) reviewed the extensive research on the progressive failure of space truss structures. The basic problem of various analytical models is that they do not satisfy the code requirements of member capacity checks, which therefore deters one from adopting them for use in actual design. The advantage of the code-based approach for strut design is that the design formula includes implicitly the member imperfections such as member initial out-of-straightness of Span Length/1000 and initial residual stresses in the cross section. Liew et al. (1997a) developed an inelastic large-displacement advanced analysis capable of capturing individual member strength and overall buckling of structure using the strut and tie model. The strut model includes three distinct axial load-shortening curves as shown in Figure 6.24. The elastic loading stage is associated with the compression of an initially imperfect column until its maximum strength Pmax is reached. The post-buckling stage is developed by assuming that a plastic hinge forms at the midspan of the member. The post-buckling unloading stage is characterized by the fact that the strut


185

Axial load, P Py

P

Linear elastic

δ

∆

P

Plastic curve

Pmax Pul

∆f

∆b

Unloading curve

∆max

Axial shortening, ∆

FIGURE 6.24 Axial load-shortening curve for a strut member (Liew et al., 1997a).

member is stretched due to the change in sign of the incremental force. It is assumed that the post-buckling unloading curve follows the elastic loading curve with the member’s imperfection magnitude computed based on the initial shortening value Δf as shown in Figure 6.24. The maximum strength of an axially loaded strut Pmax can be made to conform to the code formulae for the design of columns by assigning an equivalent initial imperfection in the member. For tie members, the axial load-elongation relationship as shown in Figure 6.25 is obtained based on the bilinear elastic-plastic stress-strain curve of the material. The main advantage of the proposed model is that member axial load-deformation relationships are developed based on the strut equations from the design specification. A separate check for member stability is therefore not required. Liew et al. (1997a) also found that the conventional structural design of performing elastic large-displacement analysis followed by individual member capacity checks may sometimes lead to the over-prediction of the limit load. If the limit load of structure is governed by the instability of individual members and not due to the accelerated geometric instability of the system because of the inclusion of member imperfections, then the overestimation of limit load by the conventional design method is acceptable.

6.2.6 Modeling of Semi-rigid Connections 6.2.6.1 Connections in Building Frame

Traditional analysis and design of steel frameworks usually assumes that the connections are either fully rigid or ideally pinned. The design of member normally becomes a separate task from that of design of the connection, which is often performed at a later stage in the overall design

186


Axial load, P

1

Py

Ep

E 1 Unloading

E 1

∆y

Axial elongation, ∆

FIGURE 6.25 Axial load-elongation curve for a tie member (Liew et al., 1997a).

process by other personnel, such as the steel fabricator. However, as is evident from experimental observations, all beam-to-column connections used in the current practice possess some stiffness that falls between the two extreme cases of fully rigid and ideally pinned. The fact that a joint has sufficient strength does not mean it has sufficient stiffness for it to be reasonably modeled as rigid. The classification methods of connections have been proposed by Section 6 of Eurocode 3 (CEN, 1992), Bjorhvde et al. (1990), and Nethercot et al. (1998). The use of semi-rigid connections in steel buildings can result in economical designs. Compared with the simple construction, semi-rigid design can reduce the floor depths and the overall volume of the building, increase the freedom for future modification and redevelopment, and result in aesthetically pleasing designs by eliminating the bracings for lateral stability. For medium and high multistory buildings, semi-rigid buildings can be designed with certain beam-tocolumn strength and stiffness for lateral stability. Furthermore, they are fast and simple to erect in contrast to the more traditional rigid-frame buildings, which typically require a substantial amount of field welding. Since semi-rigid design allows lower connection moment compared with rigid connection, it can readily lead to cost savings, possibly outweighing the extra cost incurred by increased members sizes and avoiding excessive deflections. Beam-to-column connections in building frameworks can be subjected to various force combinations such as moment, shear, axial force, torque, bimoment, and their corresponding deformations. However, research on 3-D joint behavior is rare and there is limited study on joint behavior under moment-shear-axial force interaction. Three main approaches to evaluate the mechanical properties of semi-rigid connections in terms of stiffness, strength, and ductility are by (1) experimental, (2) numerical, and (3) analytical means. The research on frame connections focuses primarily on their in-plane behavior. The most established data reported in the literature are the M-θr relationships of connections used in building construction. Although numerical studies of the connection behavior using finite element techniques have been reported by Krishnamurthy and Graddy, (1976); Bursi and Jaspart, (1997); Sherbourne and


187

Bahaari, (1997); Swanson et al. (2000); van der Vegte and Makino, (2004); and Komuro et al. (2004), the time and cost involved as well as the uncertainty inherent in the analysis render these analytical techniques unacceptable for practical use. The only practical option for the designers is the analytical approach. Analytical procedures have been developed that enable a prediction of the joint response based on the knowledge of the mechanical and geometrical properties of the joint component. Several analytical models have been developed to curve fit the experimental data with simple expressions, such as the B-spline model, polynomial model, and exponential models, etc., which are summarized in Nethercot and Zandonini (1989), Chen and Lui (1991), Chen et al. (1996), and Faella et al. (2000). A three-parameter power model was proposed by Kishi and Chen (1986) and Kishi et al. (1993) for four types of connections—single web-angle connections, double web-angle connections, top-and-seat angles with double web-angle connections, and top-and-seat angles without double web-angle connections. The initial connection stiffness and ultimate moment capacity of the connections are determined by a simple analytical model, and the empirical equation for shape parameter is calibrated to experimental results. However, this three-parameter power model may not be suitable for estimating the M-θr behavior of end-plate type connections because clear-cut strain-hardening stiffness has been observed through testing. The four-parameter power model can be used instead to represent the M-θr curves of semi-rigid connections with strain-hardening stiffness. Kishi et al. (2004) extended the three-parameter power model to the four-parameter power model for end-plate connections. The four-parameter power model is given by (Richard and Abbott, 1975): M=

(R

)

− Rkp θr [1 + Rki − Rkp θr / M 0

(

ki

)

n

] 1/ n

+ Rkpθr

(6.53)

where Rki is initial stiffness of connection, Rkp is strain hardening stiffness of connection, M0 is a reference moment, and n is shape parameter (Figure 6.26). The evaluation procedure for the four parameters in Equation 6.53 for the best representation of the M-θr curves has been provided by Attiogbe and Morris (1991). By differentiating Equation 6.53 with respect to θr, the tangent stiffness of the connection can be obtained. To allow for the

M 1

Rki

M0 Mn

1

1

Rkp

Rk

Rki 1 Connection unloading

0.02 FIGURE 6.26 Four-parameter power model.

M

θr

θr

188


unloading of the connection associated with nonproportional loading and inelastic force redistribution, the unloading stiffness is assumed to be equal to the initial stiffness as shown in Figure 6.26. 6.2.6.1.1 Component Method A more general approach that can be applied to any type of steel or composite joints is termed the component method (Annex J of Eurocode 3, 1992; Tschemmernegg and Huber, 1996; Faella et al. 2000; Liew et al., 2004). An attempt to extend the component method for predicting the 3-D behavior of steel joints under arbitrary loading is reported in Da Silva (2008). The component model considers any connection as a set of individual basic components, which is shown in Figure 6.27. The application of the component model includes three steps:

1. Identification of the active components in the connection being considered 2. Evaluation of the stiffness or resistance characteristics for each individual basic component (specific characteristics are initial stiffness, design resistance, or the whole deformability curve 3. Assembly of all the constituent components and evaluation of the stiffness or resistance characteristics of the whole joint 1. Column web panel in shear

2. Column web in compression

3. Beam flange and web in compression

4. Column flange in bending

V

Ft Fc

Fc

V 5. Column web in tension

6. End-plate in bending

Ft

Ft

9. Bolts in tension 10. Bolts in shear

Ft

7. Beam web in tension

8. Flange cleat in bending

Ft

Ft

11. Bolts in bearing 12. Plate in (on beam flange, tension or column flange, compression end-plate or cleat) Ft

Fv Fb

FIGURE 6.27 List of components covered by Eurocode 3 (1992).

Fc


189

The application of the component method requires sufficient knowledge of the behavior of the basic component. Those covered by Eurocode 3 (CEN, 1992) are listed in Figure 6.27. The application of the component method for a specific case of a welded beam-to-column connection is illustrated in Figure 6.28. Based on different analysis method, the M-θr curves obtained by the component method can be idealized as:

1. A linear curve for elastic verification of the joint resistance and plastic verification for joint resistance 2. A rigid-plastic curve for a rigid-plastic analysis 3. A nonlinear curve for an elastic-plastic analysis

Similar developments for the design evaluation of semi-rigid steel frame in the framework of the AISC Direct Analysis was proposed by Surovek et al. (2005). Component Method Three steps

F M F

First step: component identification

Second step: component response

Column web in shear

Column web in compression

F R1

F

Column web in tension

F

R2

R3 Ek2

Ek1 ∆1

Ek3

∆2

∆3

Stiffness coefficient ki of each component Resistance Ri of each component Third step: component assemblage

M MR ke

θ

FIGURE 6.28 Application of the component method to a welded joint.

190


6.2.6.1.2 Computer Implementation There are three different ways to incorporate the connection flexibility into the computer-based structural analysis of steel frameworks. The first is to introduce additional connection elements (or physical rotational spring elements) that model the beam-to-column connections directly. One drawback of this approach is that modeling effects are increased to incorporate an additional node at each element end with semi-rigid connection. In the second approach, the element stiffness matrix is modified to account for connection flexibility, i.e., in the refined plastic analysis proposed by Liew et al. (1993b). In the third approach (Hsieh and Deierlein, 1991; Chen et al., 2000), the corresponding local rotational degrees of freedom (DOF) between the member end and connection are treated as additional global unknowns of the structural system and are included in the global equilibrium equations. To introduce the local DOF into the global solution system, the conventional element transformation matrices are modified for the elements with semi-rigid connections. The modified matrices are used to transform the element stiffness matrices from the local to the global coordinate system with some of the unknowns retaining their local coordinate reference axes. A key advantage of this approach is that the existing nonlinear formulation for the beam-column elements is unaffected. This avoids the difficulty (particularly for 3-D problems) of directly formulating the connection flexibility into the nonlinear element stiffness matrices. The use of separate connection elements also facilitates further modifications to the connection model.

6.2.7 Modeling of Tubular Joints

The joints in tubular steel frames—particularly the simple and unstiffened joints—may exhibit considerable flexibility in both the elastic and elastic-plastic ranges. Some joints may reach their ultimate strength and cause excessive deflections and different internal force distribution in the structure. Depending on the joint geometry, the capacity of the connection between brace and chord may be less than the brace capacity. This means that the brace cannot be fully utilized. To take these into account, the conventional method (Qian, 2005) is to use shell or solid elements to model the joint. However, this treatment is normally for the detailed numerical study of the joint behavior and may not be suitable for the global nonlinear analysis of the frame system due to the time required to prepare the input as well as the extensive computer time required.

6.2.7.1 Joint Capacity

A joint model based on the simple elements with elastic-plastic behavior can be adopted to overcome this difficulty (Ueda and Rashed, 1991; Hellan, 1995; Dai, 2002). For thick-walled tubular sections used extensively in jackups, simplified joint stiffness and strength formulations have been developed by Choo et al. (2005) through the calibration to FEM analyses. For a K-joint as illustrated in Figure 6.29, two extra nodes are added at the brace to chord intersection face and two extra elements are generated at the end zone of the braces. A plastic hinge is formed at the extra node of the extra element is the forces satisfy the API joint capacity equation (API RP 2AWSD, 2002): 2

2

π P   Mi   Mo  Φ = cos   − M  +M  =0 2 P   iU   oU  U 

(6.54)

in which PU is the ultimate axial capacity, MiU is the in-plane ultimate moment capacity, MoU is the out-of-plane ultimate moment capacity, P is axial force, Mi is the in-plane moment, and Mo is outof-plane moment. For braces that carry part of their load as K-joints and part as T&Y or X-joints, the calculation of capacities PU, MiU, and MoU should be based on the weighing factors according to the portions in the brace classification (API RP 2A-WSD, 2002).


191

Brace 2 extra elements

Beam-column element 2 extra nodes

Beam-column element Brace

Chord

FIGURE 6.29 Modeling of a joint in tubular steel frame.

6.2.7.2 Parametric Equations for Local Joint Flexibility

When a tubular joint is loaded, the chord wall will deform and the local flexibility of the joint may be modeled by rotational and translation springs as shown in Figure 6.30. In principle, the local joint flexibility of a single-brace tubular joint should be given by a 6 × 6 matrix corresponding to three forces and three moments applied at the end of brace. However, the two shear forces and the torque are irrelevant to joint design, therefore reducing the flexibility matrix to a 3 × 3, which includes only the axial force and the in-plane and out-of-plane bending moments. The off-diagonal terms of this reduced matrix is either uncoupled, as is the case between in-plane and out-of-plane degrees of freedom, or small enough to be ignored for the analysis purpose. When two-brace joints are considered, the flexibility matrix is expanded to a 6 × 6 matrix and some carryover terms are included. The concept of the flexibility matrix also can be expanded to a joint with more than two braces (Dai, 2002). The local joint flexibility is a function of the relative sizes of the through member (chord) and the attaching members (braces), as well as of the load pattern acting on the braces. Theoretical and experiment works have been carried out to find the method for determining the local flexibility of tubular joints. A number of parametric formulae for evaluating the local joint flexibility

P

M

θ

δ

FIGURE 6.30 Local flexibility of a tubular joint modeled by rotational and translation springs.

192


have been proposed since the 1980s. The formulae of Fessler (Fessler et al., 1986a, b), Chen (Chen et al., 1990), and Buitrago (1993) cover a relatively wide range of parameters and can be utilized in the global structural analysis. The main limitation of Fessler’s and Chen’s equations is that they cannot deal with joints with equal brace and chord diameters, which is quite common for practical frames with X-joints. To solve this problem, Buitago’s equations can be used.

6.2.7.3 Load-deformation Relationship

The load-deformation relationship of joint flexibility can be idealized as bilinear or trilinear models as shown in Figures 6.31 and 6.32 (Dai, 2002). Pʹy and Pʹu are the yielding axial strength and ultimate axial capacity of the joint when the joint is simultaneously subjected to an in-plane moment M and can be derived using the following equations:

 π Py′  M − cos   =0 My  2 Py 

(6.55)

 π P′  M − cos  U  = 0 MU  2 PU 

(6.56)

The ratio a = Py /PU = My /MU = Py′ PU′ = M y′ MU′ is obtained from the test results and can be chosen as a constant. For K, Y/T-joints, a = 0.8. For X-joints, a = 0.6 (Dai, 2002). In the trilinear model shown in Figure 6.32, K axial ′ and Rki′ can be chosen as a third of the elastic stiffness (Kamba, 1997). For axially loaded joints, Yura et al. (1980) proposed a deformation limit beyond which joint failure is said to have occurred. The Yura deformation limit δmax is taken to be equivalent to the change in length of an unconnected brace member of length lb = 30d under axial loading and with a strain of twice the uniaxial yield strain εy, i.e., δmax = 2εy × lb. For brace length of 30d and εy = fy /E ( fy = yield strength, E = Young’s Modulus), δmax = 60d fy /E. For in-plane bending loaded joints, the Yura rotation limit is taken to be equal to that occurring at the ends of a simple supported, unconnected brace member of length lb = 30d subjected to transverse, uniformly distributed load of sufficient magnitude to cause beam bending strain of 4εy. Using the Yura recommendation that lb = 30d, the resulting rotation limit θmax = 80fy /E. M

Pu

M=0

Mu

P=0

P'u

M=0

M'u

P=0

In-plane moment

Axial load

P

Kaxial

a

Rki

Axial deformation

δmax

δ

b

In-plane rotation

θmax

FIGURE 6.31 Bilinear load-deformation relationship: (a) axial load vs. axial deformation; (b) moment vs. rotation.

θ


P

M

M=0

Mu

M=0

My M'u

K'axial

Py P'u P'y

In-plane moment

Axial load

Pu

P=0 R'ki

P=0

M'y

Rki

Kaxial

a

193

Axial deformation

δmax

δ

b

In-plane rotation

θmax

θ

FIGURE 6.32 Trilinear load-deformation relationship: (a) axial load vs. axial deformation; (b) moment vs. rotation.

6.2.8 Tubular Frame with K-type Joints

Figure 6.33 shows a tubular frame with K-type joints tested by Bolt et al. (1994) and later analyzed by Dai (2002). The frame is subjected to a horizontal load P at the right top. The finite element models with and without considering initial imperfections are shown in Figure 6.34. The structure is analyzed by assuming both the rigid connection and semi-rigid connection with bilinear and trilinear models. The load displacement curves generated from the second-order plastic-hinge analysis are compared with the test results as shown in Figure 6.35. The initial stiffness, ultimate load and the load level of the first plastic hinge of the structure predicted by different analysis methods are compared to the test results in Table 6.2. It can be concluded that:

1. By neglecting the joint flexibility, the rigid frame analysis (rigid joint model) with and without considering the joint size predicts stiffer load deformation curves and higher ultimate strength than do the test results. The rigid frame analysis with zero joint size and without initial imperfection predicts the initial stiffness and ultimate load of 28.7 percent and 41.3 percent higher than those from the test. 2. For the semi-rigid models, there is little difference when bilinear or trilinear connection models are used. Both semi-rigid models can predict flexible load deformation curves that closely match the test result. 3. Modeling of member initial imperfection has shown some difference on the results predicted by the rigid joint model. However, for frames with semi-rigid joint models, the effects of member initial imperfection are negligible. 4. The semi-rigid models can predict the ultimate load with good accuracy in comparison with the test result with an error less than 2.5 percent. 5. The yielding of the K-joint is predicted as observed in the actual test when the joint performance is modeled in the analysis. 6. The effects of the joint performance are of most importance to this frame.

194


UB610x229x140, f y =320 N/mm

2

P

δ0 = L/1000

168/4.5/290

356/12.7/350

356/12.7/350

168/4.5/290

168/4.5/290

a

δ0 = L/1000

168/4.5/290

UB356x368x202, f y =320 N/mm

2

Note: 356/12.7/350 Outside diameter = 356 mm Wall thickness = 12.7 mm 2 =350 N/mm fy

b

FIGURE 6.33 Frame with K-type joints

FIGURE 6.34 Finite element model: (a) with initial imperfection; (b) without initial imperfection.

800 Rigid connection with finite joint size (δ0 = 0)

700

Load, P (kN)

600

Rigid connection with zero joint size (δ0 = 0)

500 400

Test

300

Semi-rigid connection with tri-linear model (δ0 = L/1000) Semi-rigid connection with bi-linear model (δ0 = L/1000)

200 100 0

0

10

20

30

Lateral Displacement (mm)

40

50

FIGURE 6.35 Global response of frame with K-type joints.


195

TABLE 6.2 Analysis results of frame with K-type joints Analysis without initial imperfection Semi-rigid

Finite rigid

Zero rigid

Bi-linear

Trilinear

Max load (kN)

675 (40.5%)

679 (41.3%)

470.4 (−2.1%)

Initial stiffness (kN/m)

25903 (36.5%)

24417 (28.7%)

Load at first plastic hinge (kN)

650

656

Analysis with initial imperfection Finite rigid

Zero rigid

470.2 (−2.1%)

603.7 (25.6%)

21500 (13.3%)

21500 (13.3%)

360

367

Semi-rigid

Test

Bilinear

Trilinear

603.7 (25.6%)

468.5 (−2.5%)

468.2 (−2.5%)

27300 (43.9%)

27300 (43.9%)

21500 (13.3%)

21500 (13.3%)

18970

554

554

360

367

—

480.4

Note: values in bracket are percentage errors compared with the test results

6.2.9 Bowstring Column

Bowstring steel columns were first investigated by Liew et al. (2001a) where the effects of geometric imperfection and cable pretension forces were considered. Chan et al. (2002) presented a stability analysis and parameter study of prestressed cable-stay columns. In Liew and Li (2006), the nonlinear behavior of pretensioned bowstring columns is examined with advanced analysis. Different structural configurations, cable pretension forces, and length and spacing of horizontal struts are examined.

6.2.9.1 Pretensioned Steel Column

Pretensioned steel columns generally comprise main column and horizontal strut and cables, as shown in Figure 6.36. The column is the main component that resists axial load, while horizontal struts and pretensioned cables work together as the intermediate lateral support to the main column. The study in this paper is carried out using only circular hollow sections for the main column and horizontal struts, due to aesthetic reasons and the fact that circular hollow section offers better resistance to lateral torsional buckling compared to H or I sections. A summary of the material properties and section size used for analysis is shown in Table 6.3. Pretensioned steel columns with a length of 10, 15, and 20 m are selected in that their slenderness ratios LV/r (83, 125, and 166, respectively) are within the general range of engineering application where Lv is the spacing of horizontal struts and r is the radius of gyration. The bottom end of the pretensioned steel columns is assumed to be restrained in three translational directions and torsion while being free to rotate. However, the support at the top of the column is free to translate in the vertical direction and rotate, but it is restrained in the other two translational directions and torsion. Initial geometric imperfection of Lc/500 magnitude is introduced to the main column (Lc is the column length). The imperfection pattern is assumed to be the same as the first buckling mode of the main column.

6.2.9.2 Structural Configurations

There are many types of cable shapes (or restraining configurations) for the pretensioned steel columns such as triangular, rectangular, and bowstring shapes as shown in Figure 6.36. The bowstring column configuration is defined by a second-order polynomial equation, which describes a parabolic curve. Configurations defined with other higher-order polynomial equations will not

196


Main column

Horizontal strut

Cables

a

b

c

FIGURE 6.36 Three types of pretensioned steel column: (a) triangular; (b) rectangular; (c) bowstring. TABLE 6.3 Summary of the material properties used for analysis of bowstring columns Elements

Material properties

Section size

Vertical strut

fy = 275 MPa E = 205 GPa

CHS 88.9 × 4.0 mm

Horizontal strut

fy = 355 MPa E = 205 GPa

CHS 60.3 × 4.0 mm

Pre-tensioned cable

fy = 460 MPa E = 150 GPa

Diameter 10 mm

fy is the design strength and E is the Young’s modulus

be included in the present analysis. The numerical examples are designed for triangular, rectangular, and bowstring columns with three lengths of 10 m, 15 m, and 20 m and with three horizontal struts uniformly spaced. The maximum length of horizontal struts at midspan is assumed as Lc/16 (Lc is the column length) for three configurations. The same cable forces of 11 kN are pretensioned for different column lengths and different column configurations. All pretensioned columns are subjected to initial geometric imperfection and axial compression force. The results of axial load capacities are listed in Table 6.4 and the corresponding failure modes are shown in Figure 6.37. The bowstring column has the highest axial load capacity as compared to the triangular shape column with the lowest capacity. The rectangular columns can be the alternative if the column has a relatively large slenderness ratio (more than 100). For a triangular cable shape, the horizontal struts at quarter-span are not fully effective, and cannot provide the lateral restrain forces


197

TABLE 6.4 Axial load capacities of different column configurations with different lengths (Unit: kN) Length 10 m

15 m

20 m

Triangular

122

94

59

Rectangular

165

115

69

Bowstring

183

121

74

Configuration

b

a

10m

15m

20m

10m

c

15m

20m

10m

15m

20m

FIGURE 6.37 Failure modes of pretensioned steel columns with lengths of 10m, 15m, and 20m: (a) triangle; (b) rectangular; (c) bowstring.

to the main column that would enable earliest buckling. Although insufficient support also exists at midspan horizontal strut due to the equal length for all struts in rectangular cable shape, this disadvantageous effect will decrease with the development of lateral deflection at midspan. A bowstring cable shape can provide harmonious lateral restrain forces to both midspan and quarter-span horizontal struts, and can give the highest load carrying capacity. Since bowstring column is the most efficient configuration, it will be used in the subsequent sections to investigate the effects of cable pretension force, length, and spacing of horizontal struts.

6.2.9.3 Cable Pretension Force

Cable pretension force is an important parameter that affects the stiffness and strength of the pretensioned steel columns. The effects of cable pretensions on the load capacity of bowstring columns with lengths of 10 m, 15 m, and 20 m are investigated. The columns studied here have three horizontal struts uniformly spaced and the maximum length of horizontal struts at midspan is assumed as Lc/16 (Lc is the column length). It is assumed that the yield stress of cable material is 460 MPa. Since the diameter of cables is 10 mm, the yielding load of the cable is about 36 kN. The bowstring columns are analyzed using advanced analysis by assuming different pretensioning forces in the cables. The results are presented in Figure 6.38 showing the axial capacity of the column versus the pretension force, which is normalized by the cable yield load Ty. Cable pretensions equal to 5 percent of cable yield load can evidently improve the column capacity when compared to the cases without cable pretensions. The preferred range of cable pretension force is

198


L = 10m

Load Capacity P (kN)

210

P

180

T0

150

15m

120 90

L

20m

60

T0

30 0

P 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Cable Pre-tension Force / Yield Load (T0 / Ty) FIGURE 6.38 Axial load capacity vs. cable pretensions for bowstring columns.

related to the column slenderness and can be found generally between 30 percent and 50 percent of cable yield strength. When the pretension force is too high (more than 50 percent of the cable yield strength) the axial capacity of bowstring columns will reversely decrease, as shown in Figure 6.38. This is because high pretensioning force in the cables introduces a high compression load on the main column, and thus reduces its load-bearing capacity.

6.2.9.4 Length of Horizontal Strut

The length of horizontal struts in bowstring columns is limited for the sake of aesthetic reasons and restraint effectiveness. By changing the length of horizontal struts of bowstring columns, its effects on the column ultimate capacities can be examined. The numerical results are listed in Table 6.5 where the three lengths of horizontal struts studied are Lc /8, Lc /16, and Lc /24 (Lc is the column length). For the 10 m-long columns, yielding of horizontal struts is not observed in numerical analysis and the longer the horizontal struts, the higher the column capacity. However, in the case of Lc /8 for 15 and 20 m-long columns, yielding of horizontal struts occurs before column failure and causes the prematured collapse of columns when compared with the case of Lc/16, as TABLE 6.5 Axial load capacities of a bowstring column of different lengths of horizontal strut and column (Unit: kN) Column length (Lc)

10 m

15 m

20 m

Lc /8

210

103

63

Lc /16

183

121

74

Lc /24

118

104

77

Horizontal strut length


199

shown in Table 6.5. If the section of horizontal struts is strengthened and replaced by CHS 80.0 × 4.0, the capacities are 135 kN and 76 kN respectively for 15 and 20 m-long bowstring columns with Lc /8-long horizontal struts, which are higher than those of Lc /16 because yielding of horizontal struts is prevented. It can be drawn from investigation in this section that horizontal struts should be adequately designed to prevent premature yielding or buckling, and when longer struts are used, more attention should be paid to the possibility of yielding or buckling of the horizontal struts.

6.2.9.5 Spacing of Horizontal Strut

The spacing of horizontal struts LV is varied as Lc /4, Lc /5, and Lc /6 for bowstring columns 10, 15, and 20 m in length. The length of horizontal struts is kept to be Lc /16 and the cable pretensioned to be 11 kN as above. The axial capacities obtained from advanced analysis are listed in Table 6.6. A general conclusion can be drawn that the more horizontal struts are provided, the higher compressive capacity—especially for the columns with relatively high slenderness ratio. This is because of the reduction in the effective buckling length of the main column between two lateral restrained points. Increasing the number of restrained points will not further increase the capacity, because the failure will be caused by the overall buckling of the bowstring column.

6.2.10 Bowstring Frame

The concept of bowstring columns can be extended to 3-D frames (Liew and Li, 2006) if the stability of support columns in the out-of-plane is ensured by bowstring cables, while that in the in-plane stability is provided by frame action. Based on the study of bowstring columns, structural behavior of a bowstring frame is analyzed in this section, where the structural layout, novel semi-rigid connection, structural nonlinearities under environmental loads, and effects of cable pretensions are addressed.

6.2.10.1 Structural Layout

A bowstring structure supporting a glass facade is shown in Figure 6.39. It consists of seven dependent frames (three on the left and four on the right) and one lateral bracing frame. The detailed model of a bracing frame is shown in Figure 6.40, which includes the elevation view in X-Y and Y-Z planes. When the bowstring frames are assembled, pretension force is applied to the bowstring cables and bracing cables to provide lateral stiffness in the in-plane and out-of-plane direction of the frame. After the roof slab and glass facade are constructed, the bowstrings are under compression and a second-stage pretension force is applied to the cables so that they can have sufficient lateral

TABLE 6.6 Axial load capacities of a bowstring column of a different number of horizontal strut and column lengths (Unit: kN) Column length (Lc)

10 m

15 m

20 m

3

183

121

74

4

194

154

96

5

196

163

113

Number of horizontal strut

200


Transom RHS 150 x 100 x 5

Hanger Mullion RHS 100 x 100 x 4 RHS 200 x 100 x 10 Roof slab

Dependent frame Bracing frame FIGURE 6.39 The structural model of bracing bowstring frame and a roof slab (Liew and Li, 2006).

Top cable: φ16 fy = 460N/mm2

Roof load C

C(B)

Outside

10 Struct:24x75 fy = 550N/mm2 wind suction

Pretensioned cable: φ30 fy = 460N/mm2

wind pressure Pretensioned cable: φ30 fy = 460N/mm2

a

Z

RHS 100x100x4 fy = 355N/mm2

A

2.0m

Bracing cable: φ24 fy = 460N/mm2

2.0m

Lateral bracing force Y X

2.0m

Y O

RHS 200x100x10 fy = 355N/mm2

2.0m

2.0m

Inside

RHS 150x100x5 fy = 355N/mm2

2.0m

glass panel

A

B

1.0m

X

1.0m

b

2.5m

2.5m

O

FIGURE 6.40 The structural model of bracing bowstring frame (Liew and Li, 2006): (a) X-Y plane; (b) Y-Z plane.

Z


201

TABLE 6.7 Loads and loading sequence in analysis Load sequence 1

Load type 1st stage pre-tension

Load description a) T ension inside and outside cables to 52 kN and 50 kN respectively b) Tension bracing cables to 10 kN a) A pply dead loads = 301 kN, at upper column points

2

Deal load

b) Apply glass facade loads of 1.75 kN/m on vertical mullions and 1.4 kN/m on transoms c) Apply self-weight

3

2nd stage pre-tension

a) T ension the inside and outside cables to 78 kN and 82 kN respectively b) Tension bracing cables to 10 kN pply bracing force at left side = 18.834 kN per a) A node

4

Lateral bracing force (see Figure 6.40)

5

Temperature effect

Temperature inside glass facade reduces 15°C and that outside increases 25°C simultaneously

Wind pressure

Apply wind pressure = 2.0 kN/m on mullions and 1.6 kN/m on transoms, up to failure

Wind pressure

Apply wind suction = 1.4 kN/m on mullions and 1.12 kN/m on transoms, up to failure

6

b) Apply bracing force at right side = 23.082 kN per node

stiffness to resist further loadings such as imposed roof load and wind load. The load sequences of the bowstring structures are tabulated in Table 6.7.

6.2.10.2 Testing of Mullion-to-transom and Transom-to-hanger Connections

Mullion-to-transom and transom-to-hanger connections of frames in-plane are designed as those of semi-rigidity. The rotational stiffness and moment capacity of these two connections are tested so that nonlinear analysis models of bowstring frames can be correctly established and then the structural behavior can be assessed. The test setup and specimen instrumentations are illustrated respectively in Figure 6.41. Test Specimen 1 represents the hanger (100 × 100 × 4 mm RHS) to transom (150 × 100 × 5 mm RHS) connection, which consists of one M24 × 60 Grade 8.8 HEX. HD. bolt connecting the 20 mm plate welded on the inside of the hanger to the 30 mm plate welded on the surface of the transom (see Figure 6.41c). Test Specimen 2 represents the mullion (200 × 100 × 10 mm RHS) to transom (150 × 100 × 5 mm RHS) connection, which consists of two M24 × 60 Grade 8.8 HEX. HD. bolts connecting a 20 mm plate welded on the inside of the transom to a 30 mm plate welded on the surface of the mullion (see Figure 6.41c). The M-θr curves obtained from the tests are shown in Figure 6.42. The test results are fitted with the four-parameter connection model in Equation 6.53 and then used in the analysis as shown in Figure 6.42. For Specimen 1, the left side of the connection is stiffer than the right. This could be due to nonsymmetry in the specimens and the fitting of connections. Failure of connection occurred

FIGURE 6.41 The test setup and specimen instrumentation of semi-rigid connections in bowstring frames (Liew and Li, 2006): (a) setup; (b) specimen instrumentation; (c) elevation view of connections; (d) A-A view of Specimen 1; (e) A-A view of Specimen 2.

a Hanger. RHS 100x100x4 (Specimen 1) or Transom: RHS 150x100x5 (Specimen 2)

P Transom: RHS 150x100x5 (Specimen 1) or Mullion: RHS 200x100x10 (Specimen 2)

Left

Right

Transducer

See (c~e) 800

800

b

Connection plate t = 30 Connection plate t = 20 A 100

100

A

Access hole 100x80

Connection bolt(s):M24x60 One bolt for Specimen 1 Two bolts for Specimen 2

100

c 20 40

40 20

30

30

10

100

100

100

30

70 40

40

202

100

100

40

10

40

30

70

150

e

100

40 20

20 40 10

100

150

d

50

50

100

50

50

10

100

100

100

100


Four parameters for Specimen 2: Rki = 460kNm/rad, Rkp = 25kNm/rad, M0 = 14.45kNm, n = 2.7

18

Moment (kN-m)

16

203

Specimen 2

14 12

Four parameters for Specimen 1: Rki = 190kNm/rad, Rkp = 15kNm/rad, M0 = 6.29kNm, n = 3.3

10 8

Specimen1

FIGURE 6.42 Momentrotation curve of semi-rigid connections: test data vs. fourparameter model in Equation 6.53 for Specimen 1 (hangerto-transom) and Specimen 2 (mullion-to-transom) (Liew and Li, 2006).

6 4

Test data Four-parameter model

2 0

0

20

40

60

80

100

Rotation (Millirads)

120

140

FIGURE 6.43 Connection detail and failure modes (Liew and Li, 2006): (a) Specimen 1 (hangerto-transom); (b) Specimen 2 (mullion-to-transom).

a

b

204


due to yielding of the transom member caused by the compression force from the hanger beam. Weld failure, as shown in Figure 6.43, was observed upon subsequent loading after attaining the maximum load. The moment capacity is about 8 kN-m. For Specimen 2, the transom-to-mullion connection failed when the flange of the transom, which connects into the mullion, yielded under compression. The moment capacity of the connection is about 17 kN-m. Failure modes of two specimens are shown in Figure 6.43. Experimental results provided reliable parameters for modeling the nonlinear rotational spring elements used in the structural analysis.

6.2.10.3 Nonlinear Analysis

By preliminary calculation, two critical load combinations of the bracing frame are identified:

1. 1.0 (dead load) + lateral bracing load + ambient temperature difference + wind pressure 2. 1.4 (dead load) + lateral bracing load + ambient temperature difference + wind suction

Lateral bracing loads in the direction of Z axis (in-plane of frame) represent the required bracing forces provided by the bracing frame to the other seven dependent frames within one loadbearing unit (see Figure 6.40 and Table 6.7). According to BS5950-1 (2000), where three or more intermediate lateral restraints are provided, each intermediate lateral restraint should be capable of resisting a force of not less than 1 percent of the compression force. For sake of simplification, only nonlinear analysis results of these two load cases are presented in this paper. The loads and loading sequences used in the analysis are listed in Table 6.7.

Pressure wind factor

2.4

C

2.0 1.6 1.2 0.8 0.4 0 -30 -20 -10

a

A

A, X-direc. (cm) C, Y-direc. (mm) A, Z-direc. (mm)

Y O Z

0

10

20

30

Nodal displacement

40

50

Suction wind factor

X

60

2.0

C

1.6 1.2

A

0.8

A, X-direc. (cm) C, Y-direc. (mm) A, Z-direc. (mm)

0.4 0 -30 -20 -10

b

Wind pressure

0

10

20

30

Nodal displacement

40

50

Wind suction

Y O

X

Z

60

FIGURE 6.44 Nodal displacement versus load factor of wind at ambient temperature: (a) wind pressure; (b) wind suction.

Load factor of pressure wind


2.4 2 1.6

Wind pressure

Outside cable Inside cable

1.2

Inside cable Outside cable

0.8 0.4 0

0

50

100 150 200 250 300 350 400 450

Cable Tension (kN)

a

Load factor of suction wind

205

2 1.6

Outside cable

Inside cable

1.2

Wind suction Inside cable Outside cable

0.8 0.4 0

0

50

100

b

150

200

250

300

350

400

Cable Tension (kN)

FIGURE 6.45 Cable tension vs. load factor of wind at ambient temperature: (a) wind pressure; (b) wind suction.

The typical load-displacement curves and cable tension variations are illustrated in Figures 6.44 and 6.45. Nonlinear structural response is observed when wind loads are applied. The nonlinearity is due to second-order effects associated with the axial force acting on the deflected geometry of the structure, the change in cable tension, and nonlinear behavior of semi-rigid connections. No plastic hinge is observed up to the structural failure, while buckling of vertical mullions occurs at the ultimate states. One of the reinforcing cables to the vertical mullions will slack soon after wind loads applied (as illustrated in Figure 6.45), but this does not trigger the collapse of the system because the other reinforcing cable is still in tension and the structure is capable of resisting more loads. Large deflections in both the X-direction and Z-direction are observed when instability occurs. But the deflection in X-direction is dominant rather than that in Z-direction, which implies that the bracing cables are providing effective lateral TABLE 6.8 Five pretension cases for stiffness in the frame plane to other dependant bowstring frames frames. Case First stage Second stage

6.2.10.4 Effects of Pretension

As mentioned above, the two-stage pretensioning technique is needed in the construction of the bowstring frames because the weight of the roof and glass facade will reduce the cable pretension forces, and the frame stiffness against wind loads will be insufficient if only first-stage pretensioning is applied. In this section, the ef-

pretension (kN)

pretension (kN)

a

0

0

b

50

0

c

50

45

d

50

80

e

50

115

206


Pressure wind factor

2.5 2 1.5

Pretension a

1

Pretension b Pretension c

0.5

Pretension d Pretension e

0 -25

-20

-15

-10

-5

0

5

Nodal displacement (cm) FIGURE 6.46 Effects of cable pretensions (see Table 6.8 for cable pretension cases).

fects of pretension forces on the capacity and stiffness of the bowstring frame, represented with five pretension cases (Case A to Case E as shown in Table 6.8) are studied. Figure 6.46 illustrates the curves of displacement in X-direction of Node A with the pressure wind factor under different magnitudes of pretension forces. Local instability has been found from the numerical results for the states of Pretension A and Pretension B, which indicates that both the first- and second-stage pretensions are both essentially necessary for bowstring structures. Pretension E does not produce an evidently higher ultimate capacity against the wind pressure when compared to Pretension D and Pretension C. The rationality of Pretension D, namely the designed pretension force, is proved as well from Figure 6.46 where a satisfied structural stiffness at nominal pressure wind load (factor = 1) is shown.

6.2.11 Fire Analysis of Semi-rigid Frame

Advanced analyses on the semi-rigid portal frame and multistory frame subjected to localized fires show that overall structures, as opposed to single elements, have a higher resistance to failure due to fire (Liew et al., 1998). This reflects the conservative nature of the traditional fire-resistant design method in which loads transferred from the fire-weakened members to other parts of the structure remote from the fire is not considered. Recent work by Bailey et al. (1996) and Liew et al. (1998) suggests that the progressive spread of fire can produce larger beam deflection than that predicted by assuming simultaneous heating of the same members in different compartments. Consequently, there exists the possibility that the structural integrity of a frame may remain intact up to its maximum temperature in a fire, but it may be lost during the cooling phase. The effect of progressive fire spread, where both cooling and heating are taking place simultaneously in different zones in a frame, is the subject for investigation. Such horizontal fire spread might happen due to nonclosure of fire doors, a breakdown of compartment walls, or even along expended surface materials such as carpets, wall linings, and ceiling linings. The structural effects of horizontal fire spread are studied within the 2-D steel frame shown in Figure 6.47. All the internal beams are made of 610 × 229UB101 with design strength 275MPa, subject to a load ratio of 0.24. All columns are of 254 × 254UC132 with design strength 275MPa. The columns are assumed to be with initial out-of-straightness of L/750 (or 5mm) at midheight. The internal columns in the fire-affected story have a load ratio of 0.18. Load ratio is defined as the axial

8m Bay 3

8m Bay 4

380.2 kN

380.2 kN

380.2 kN

190.1 kN

8m Bay 6

8m Bay 7

8m Bay 8

8m Bay 9

All beams are 610x229x101UB, Grade 43, 3-side exposed to fire. All columns are 254x254x132UB, Grade 43 & fire protexted.

8m Bay 5

Fire spread w = 23.76 kN/m

w = 23.76 kN/m

380.2 kN

w = 23.76 kN/m

380.2 kN

Fire spread

380.2 kN

Temperature gradient

8m Bay 2

380.2 kN

FIGURE 6.47 Modeling of horizontal fire-spread in a multistory semi-rigid frame.

8m Bay 1

380.2 kN 3.6 m 3.6 m 3.6 m 3.6 m

190.1 kN

Advanced Analysis of Steel and Composite Semi-rigid Frames 207

208


force divided by the compression resistance of the member. It is assumed that all connections are fully protected so that the connections have been prevented from reaching their ultimate strength before fire spread. The M-θr curve for the beam-to-column connections is shown in Figure 6.48. The columns and connections are fully protected and the only heated members are the beams. The beams support the concrete slabs, and hence they are modeled as three sides exposed to fire. Two elements are used to subdivide the beam web plate in the heat transfer computation, and one element per member is adopted for modeling the structural frame.

50

Moment (kNm)

40 30 20 10 0

0

20

40

60

80

100

120

Rotation (millirad) FIGURE 6.48 Moment-rotation curves for the beam-column connections in fire spread study (El-Rimawi et al., 1995).

Temperature ( C)

800

600 Bays 4&6

400

0

Bays 3 and 7

Bays 5

200

0

50

100

150

200

250

300

350

Time (mims.) FIGURE 6.49 Temperature-time relationship of fire scenario 1: spread of fire in a story (Liew et al., 1998).


209

Two fire scenarios are considered. The first involves fire spreading from Bay 5 into Bays 4 and 6, continuing into Bays 3 and 7 in accordance with the time-temperature curves in Figure 6.49. The second fire scenario assumes a simultaneous heating of the beams in Bays 3 to 7 in the second story in accordance with the temperature-time curve in Figure 6.50; the beams in Bays 1, 2, 8, and 9 remain unheated.

Temperature ( C)

800

600 All bays 400

200

0

0

50

150

100

200

250

Time (mims.) FIGURE 6.50 Temperature-time relationship of fire Scenario 2: simultaneous heating of all bays (Liew et al., 1998). 0.60

(0.576m) Beam in Bay 5 (Source Bay)

Midspan Deflection (m)

0.50

Simultaneous heating

0.40

(0.441m) L/20

Beam in Bay 4&6 Beam in Bay 5

0.30

Beam in Bay 4&6

0.20

Beam in Bay 3&7 (0.232m) (0.189m) (0.176m)

(0.198m)

Fire spread

0.10

Beam in Bay 3&7 0 0

15

30

45

60

75

90

105

Time (minute) FIGURE 6.51 Comparison of midspan deflections of the heated beams.

120

135

150

210


The displacement-time relationships of the heated beams for the two fire scenarios are compared in Figure 6.51. When the spreading of fire is considered, the vertical displacement of the beam in Bay 5 does not reduce in magnitude after reaching the peak temperature in 36 minutes. In fact, the deflection continues to increase up to a calculated displacement of 576 mm at 62.6 minutes. An explanation of this behavior is given in Figure 6.52, which shows the axial force-time relationship of the heated members. In the case of fire spread, it can be observed that the axial compression in the beam at Bay 5 decreases when the temperature approaches its maximum value at 36 minutes. When Bay 5 enters into the cooling phase, the beam in Bay 4 begins to heat, adding compression to the beam in Bay 5, thus increasing its vertical displacement. The deflection of the beam in Bay 5 does not reduce until the axial forces in Bays 4 and 6 begin to reduce at 62.6 minutes. The final residual displacement of the beam in Bay 5 is about 441 mm. It is observed that the final residual displacements of the beams in Bays 4 and 6 and Bays 3 and 7 are not significantly affected by fire spread, with an average calculated deflection of approximately 180 mm. In the case of uniform heating, the maximum beam deflections at Bay 5, Bays 4 and 6, and Bays 3 and 7 are 382, 397, and 366 mm, respectively. These occur at approximately 36, 34, and 39 min, respectively. The final residual beam deflections are 306 mm for Bay 5, 298 mm for Bays 4 and 6, and 286 mm for Bays 3 and 7, and they do not differ significantly. It can be observed from Figure 6.52 that all the heated beams in Bays 3 to 7 experience compression during the heating phase and the initial cooling phase for about 50 minutes. These beams are in tension in the subsequent cooling phase (i.e., when the time is greater than 50 minutes). It is noticed that the peak value of compression does not take place at the same time as the maximum temperature. The compression forces in the members increase with the temperature for the first 24 minutes, after which the compression forces start to decrease even as the temperature keeps increasing. This is because the plastic strength surface contracts at elevated temperatures. Since the force state (axial force and moment interaction) is not allowed to exceed the plastic strength surface after it has reached the cross-section plastic capacity, it has to remain on the plastic surface during subsequent heating.

Beam in Bay 5

Midspan Axial Force (kN)

2000

Beam in Bay 4&6

Simultaneous heating

1000

Beam in Bay 3&7 Beam in Bay 5 (Source Bay)

Tension

0 -1000

(751kN, Bay 5)

Fire spread

-2000 -3000 0

Compression Beam in Bay 4&6 (985kN, 3&7) Beam in Bay 3&7

(798kN, 4&6)

15

30

45

60

75

90

Time (minute)

105

FIGURE 6.52 Comparison of midspan axial forces of the heated beams.

120

135

150


211

Hence, the compression forces decrease as a result of the contracting of the plastic surface during heating. In comparison, the beam in Bay 5 has been significantly affected by fire spread. The maximum and residual deflections of Beam 5 are larger than the limiting deflection of span L/20 when the fire spread has been taken into account, but neither is so in the case where a constant time-temperature relationship is assumed. The analysis shows that the frame can survive in the fire scenario when all bays in the story are heated simultaneously, but not in the case when fire spreading is modeled. It is, therefore, important to consider the possibility of fire spread in the event of fire when the stability of the building is to be maintained for a reasonable period of time; otherwise the walls or partitions of the building must be so constructed that, in the event of fire, they are effective in preventing the spread of fire from one compartment to another.

6.3 Advanced Analysis of Composite Frames Modern high-rise buildings constructed in recent years have adopted composite structural systems combining the use of concrete core wall and steel framing to provide a cost efficient design (Liew, 2001a, 2001b, 2004; Liew and Uy, 2001; Uy and Liew, 2002; Liew and Chen, 2004a). One of the distinctive features of composite floor construction is to design the steel beams to act compositely with the concrete floor slabs by means of the shear connectors. When building frames are subject to gravity and lateral loads, the distribution of the bending moment in the composite beams varies along the member length. In the hogging (negative) moment region, the concrete in tension is cracked and the steel reinforcement in the slab is subjected to tension offering resistance to hogging moment. In the sagging (positive) moment region, a large bending moment may cause partial yielding of the steel section and crushing of the part of the concrete slab. Consequently, the flexural stiffness of beams varies along the member length. To accurately predict the limitstate behavior of the overall system, the elasto-plastic nonlinear behavior of the composite members must be considered. The use of continuum finite elements for the analysis of composite beams is computationally too intensive for large-scale structures. The cost and effort of such a method is so great that they often prohibit analysis of a complete framework. To reduce the computational effort, Liew et al. (2001b) proposed a composite beam model to study the inelastic behavior of composite floor beams. The flexural stiffness of a composite beam segment can be evaluated, including the effects of partial shear stud interaction between the concrete slab and the floor beams. For high-rise buildings, concrete core walls are often used to provide torsional and flexural rigidity and strength with or without the participation from the frame system. Conceptually, a central core with punched openings for lift access is used to provide a cantilever action for lateral load resistance. The floor framing is arranged in such a way that it distributes enough gravity loads to the core walls so that the design of the core is controlled by compressive stresses even under high lateral forces. Structural core walls provide an efficient type of lateral load resisting system up to a certain height premium because of their cantilever action. However, when it is used alone, the massiveness of the core increases with height, thereby inhabiting the free planning of interior spaces, especially in the core area. The space occupied by the core walls leads to loss of overall floor area efficiency as compared to tube system, which could otherwise be used. This section examines the nonlinear behavior of a combined system of concrete core wall and perimeter frames to form an efficient lateral system for high-rise construction. Previous research on advanced analysis in steel framed structures is limited in its application unless the effects of concrete infill or encasement and concrete slabs can be considered. This section reviews the current trend in advanced analysis of composite members, composite con-

212


nections, and frames. In undertaking this review, the types of advanced analysis for frames are summarized by tracing the progress that has been made in the advanced analysis of steel structures. This section also indicates the pertinent areas that need to be considered in order to bring the methods of advanced analysis of composite frames into wider circulation. Several illustrative examples are given to show the benefits of using advanced analysis for the design of real-size framework. Assessment of the building performance with respect to its load displacement behavior, serviceability, and ultimate-limit states are conducted.

6.3.1 Composite Members—Advanced Analysis

While there has been considerable research into the behavior of steel frames and advanced analysis, composite frames have received less attention until recently. Eurocode 4 (CEN, 1994) for example, makes no mention of this type of analysis procedure and it is largely a prescriptive-based code. Chen et al. (2000) developed a thin-walled beam-column element allowing for the advanced modeling of concrete core-walls and their interaction with the surrounding steel frames. Liew et al. (2001b) have developed an advanced inelastic analysis technique and applied it to considering multistory steel buildings with composite beams. In trying to perceive future developments, it is worth highlighting some of the potential areas, which may need consideration in order to make the methods of advanced analysis robust and thus able to be used widely for the design of composite structures. Some of the potential areas that may need consideration include:

1. 2. 3. 4. 5.

Local and overall buckling of composite members Distortional buckling Lateral torsional buckling Limited slip capacity Rotational capacities

FIGURE 6.53 Local buckling of concrete-filled steel columns (Uy, 2000).


213

6.3.1.1 Local and Overall Buckling of Composite Members

In order to model the inelastic response of composite structures accurately, the effects of local and overall buckling of composite members must be considered. Uy (2000, 2001) has considered the effects of local buckling on concrete-filled steel columns and for composite sections in a generic manner. Figure 6.53 shows a set of typical short column specimens that have failed by local 1.2 1.0 0.8

be b

0.6 0.4

Experiments AS 4100 (1990) - HW

0.2 0

AS 4100 (1990) - LW

0

20

40

60

80

b t

a

100

120

140

160

180

200

fy 250

1.2 1.0 Experiments

0.8

be b

AS 4100 (1990) - HW AS 4100 (1990) - LW

0.6 0.4 0.2 0

b

0

20

40

60

80

b t

100

120

140

160

180

200

fy 250

FIGURE 6.54 Local buckling of concrete-filled steel columns (Uy, 2000).

214


30 25

pr

20 15 10

250 MPa 350 MPa 690 MPa

5 0 60

80

100

120

a

140

(b/t)

160

180

200

1.2 1.0

αlb

0.8 0.6 0.4

250 MPa 350 MPa 690 MPa

0.2 0.0 60

80

b

100

120

140

(b/t)

160

180

200

FIGURE 6.55 Interaction buckling of concrete filled steel columns (Vrcelj and Uy, 2002).

buckling. Figure 6.54 highlights the beneficial effects of including the concrete restraint when considering local buckling for these members. Vrcelj and Uy (2002) have considered the effects of interaction (coupled local and global) buckling effects for slender concrete-filled steel columns. Typical results are given in Figure 6.55 to highlight the effects of local buckling on the overall column buckling capacity. Furthermore, local buckling effects may also need to be considered in composite beams in both sagging and hogging moment regions when noncompact sections are used (Bradford, 1986). In some cases, this can be more critical in continuous composite beams with semi-rigid connections as large compressive forces are entirely transferred through the lower compressive flanges.

6.3.1.2 Distortional Buckling

For intermediate buckling of half-wavelengths between those for localized buckling and lateral buckling, distortional modes can develop as illustrated in Figure 6.56. This is particularly the case


215

when dealing with the hogging moment regions of continuous composite beams in frames with compact flanges. In these situations, the concrete slab provides sufficient restraint to the top flange and the web is thus forced to fail in a distortional manner. This has been receiving ongoing research, and significant developments are now currently available (Johnson and Bradford, 1983; Bradford and Gao, 1992; Vrcelj et al., 1999).

6.3.1.3 Lateral Torsional Buckling

The effects of inelastic flexural-torsional FIGURE 6.56 Interaction buckling of concrete-filled buckling in steel frames have limited steel columns (Vrcelj et al., 1999). the development of advanced analysis and this will equally be the case for composite frames. Furthermore, the flexural-torsional behavior of composite beams in hogging moment regions needs attention in order for the proper development of advanced analysis procedures. Lindner (1998) has considered the effects of lateral torsional buckling of composite beams and has determined that this can only be critical for continuous composite beams near the internal supports. Methods of providing restraint to compression flange are shown in Figure 6.57, including a strut tied to the slab and a full-depth web stiffener to provide a moment resisting U-frame action.

6.3.1.4 Limited Slip Capacity

One other important factor that has only started to receive attention, is the effect of limited slip capacity. In many of the studies dealing with the strength of composite beams, it is assumed that the shear studs have unlimited ductility. Oehlers and Sved (1995) have considered the effects of limited slip capacity for simply supported beams. Figure 6.58 highlights the effects of limited slip capacity, which can lead to premature failure of the studs prior to reaching the plastic moment capacity of the beam. This has been recently augmented by Diedricks et al. (2000) for continuous members. In order to model the inelastic response of composite frames, it is important that slip displacements are checked and that the advanced analysis methods are amenable to this. A model developed by Fang et al. (1999, 2000) allows for these details to be determined using a single element.

a

b

FIGURE 6.57 Methods of preventing lateral-torsional and distortional buckling: (a) strut tie to slab; (b) full-depth web stiffener.

216


Equilibrium Method

Moment Capacity (kNm)

Mfsc

Ms

FIGURE 6.58 Limited slip capacity model (Oehlers and Sved, 1995).

D

C

A

B

Interpolation Method

Mfrac (Mathematical Model) 1.0 Degree of Shear Connection (η)

6.3.1.5 Rotational Capacities

Another important issue that needs to be incorporated in the advanced analysis of composite frames is the issue of both available and required rotations. In order to ensure the plastic collapse behavior of beams in frames with semi-rigid or rigid connections, it is important to check that the rotations required to be developed in the hogging and sagging moment regions are able to be achieved by the connection and beam, respectively. Recent research by Kemp and Nethercot (2001) has provided an excellent platform for implementing this in advanced analysis methods.

6.3.2 Modeling of Composite Column

Shanmugam and Lakshmi (2001) carried out a state-of-the-art review on the research of steelconcrete composite columns. Emphasis is given on experimental and analytical work. Experimental data has been collected and compiled in a comprehensive format listing parameters involved in the study. The review also includes research work that has been carried out to date, accounting for the effects of local buckling, bond strength, seismic loading, confinement of concrete, and secondary stresses on the behavior of steel-concrete composite columns. Saw and Liew (2000) presented the design assessment of concrete encased and concrete-filled composite columns based on the approaches given in the European (EC4), British (BS5400), and American codes (AISC-LRFD). This includes studies on the design parameters, comparison of the nominal strength predicted by the three codes, and comparison of the predicted strengths with the available test results. The studies concluded that the results obtained from the three codes vary considerably. This is because of the different design considerations adopted in these codes. However, the design methods are found to be mostly conservative when compared with the test results. The use of advanced analysis to capture the direct effect of plasticity and stability would alleviate the need to calculate individual member strength check, while providing more information on the structural performance than do the elastic analysis or design procedures. Concrete-filled tubes are often preferred for the construction of high-rise buildings because of their high strength and stiffness compared to conventional reinforced concrete or steel columns. However, prior to infilling of concrete, the steel tubes are subjected to preloads from upper floors arising from construction loads and permanent loads of the building. These preloads cause initial stresses and deformations in the steel tubes, which would affect the load carrying capacity of the


217

composite columns. Liew and Xiong (2009) studied the effects of preload on the axial capacity of concrete-filled composite columns and proposed a design method based on a modified Eurocode 4 approach, incorporating the effect of preload, to evaluate the axial capacity of concrete-filled composite columns. Eight full-scale composite column specimens were tested. Parameters studied included the strength of the concrete infill, slenderness of the columns, and the amount of preload applied on the steel tubes. Hajjar and Gourley (1997) present a geometrically and materially nonlinear formulation to simulate the behavior of 3-D concrete-filled tubes (CFTs) subjected to monotonic static or cyclic seismic loading. The plasticity model adopts a two-surface plastic-hinge formulation with a polynomial expression for modeling the cross-section strength. Isotropic and kinetic hardening are proposed that are geared to capture the strength degradation, stiffness degradation, varnishing elastic zone, and Bauschinger effect exhibited by CFTs subjected to cyclic loading. El-Tawil and Deierlein (2001) extended the two-surface plastic-hinge model for the advanced analysis of encased composite section. Key features of their proposed models are the flexibility-based element formulation and the bounding-surface representation of the cross-section response that permit efficient simulation of inelastic cyclic behavior. By relying on force-interpolation functions that are relatively invariant to inelastic action, the flexibility approach is more accurate than conventional stiffness formulations that rely on displacement shape functions. The bounding-surface representation of stress-resultant versus generalized strain response avoids the computationally intensive integrations through the member cross section. Summarized in this paper is the development of default modeling parameters for bisymmetric steel, reinforced concrete, and composite members representative of modern building design practices.

6.3.3 Modeling of Composite Beam

For a composite beam with sufficient skip and rotational capacities that is prevented from local, distortional, and lateral torsional buckling, Liew et al. (2001b) proposed a computational efficient model for studying the 3-D behavior of building frames. The composite beam is subdivided into several segments to capture the varying flexural stiffness along the member length. The instantaneous flexural stiffness of a composite segment is derived using the moment curvature (M-Φ) relationships, thus discretization of the cross section is not required. A closed form M-Φ relationship proposed by Li et al. (1993) for a composite beam section with full or partial shear connections has been adopted in the present analysis model. For the composite beam section under positive moment as shown in Figure 6.59a, the M-Φ relationship is given by:

Φ (M ) =

M , EI

Φ (M ) =

M   M − My  M  +  Φu − u    , EI  EI   M u − M y 

0 ≤ M ≤ My

(6.57a) 2

M y < M ≤ Mu

(6.57b)

where EI is elastic flexural stiffness of the composite section under the positive moment, E is the elastic modulus of steel, My and Mu are the yield moment and the ultimate moment, respectively, and Φu is the curvature at the ultimate moment given as:

Φu = βΦy = β

My EI

(6.58)

in which D and Ds are the depths of the steel beam and the slab, respectively. Numerical analysis of composite frames with partial shear-stud interaction by one element per member has been carried out by Fang et al. (1999, 2000). In the present approach, the elastic

218


Be

Be

Rebar Ar

Ds

Concrete slab

Dp

D

a

tf

tw

Steel section

tf

Bf

Be : effective width of slab Ds : overal slab depth D : depth of deck profile

b

FIGURE 6.59 Composite beam sections: (a) positive moment region; (b) negative moment region.

flexural stiffness of composite beam with partial shear interaction under the positive moment is calculated based on the code specified equation (AISC, 1993): EI = EI s +

N EI f − EI s Nf

(

)

(6.59)

in which EIf is flexural stiffness of the composite beam with full shear connection, EIs is flexural stiffness of the steel section, and N/Nf is degree of shear connection. The instantaneous flexural stiffness of the composite beam section under the positive moment may be obtained by differentiating the moment with respect to the curvature as:

EI t = EI , 0 ≤ m ≤ α y

EI t =

(

(6.60a)

EI

) ( m − α ) / (1 − α )

1 + 2 βα y − 1

y

2

, αy < m ≤ 1

y

(6.60b)

in which m is the moment ratio (= M/Mu) and αy is the yield moment ratio (= My /Mu). For the negative moment region (see Figure 6.59b), it is assumed that once cracked, the concrete slab does not contribute to the beam’s resistance. Applying the same rule for the positive moment region, the M-Φ relationship under the negative moment is (Liew et al. 2001b): M′ , 0 ≤ M ′ ≤ M y′ EI ′

Φ ′(M ) =

M ′   M ′ − M y′  M′  Φ ′(M = +  Φu′ − u    , M y′ < M ′ ≤ M ′ EI ′  EI ′   M u′ − M y′ 

(6.61a) 2

)

(6.61b)

in which:

Φu′ = 5.3Φy′ + 2.4 = 5.3

M y′

EI ′

+ 2.4

(6.62)

The variables with prime (ʹ) have the same meaning as defined in Equation 6.57, except that here they refer to the negative moment region. In determining EIʹ, M y′ , and M u′ , the contribution of the effectively anchored rebars located within the effective width of the concrete slab as shown in Figure 6.59 can be included and the concrete slab in tension is ignored. Equation 6.61b can be used to evaluate the flexural stiffness of the composite beam under the negative moment by differentiating Mʹ with respect to Φʹ.


219

Studies by Liew et al. (2001b) show that the ultimate-limit load of steel frames while considering the composite beam action is about 30 percent higher than that of the pure steel frame. The lateral stiffness can also be significantly enhanced by considering the composite beam action.

6.3.4 Modeling of Building Core Wall

A core-braced frame system represents an efficient form of a structural system up to a certain height where the predominant lateral load resistance is provided by concrete core walls (Iyengar, 1979; Iyengar et al., 1992; Liew, 2001a, 2004; Viest et al., 1997; Taranath, 1988, 1998). In prismatic office towers of normal floor size, core walls are usually planned at the central location. In office buildings with large floor areas, core walls may exit at different isolated locations. The basic concept is for the core walls to resist all the lateral forces. The steel frameworks around the core walls are generally designed only for gravity loads with simple connections between beams and columns. The steel beams are connected to core walls either by a typical corbel detail, or by bearing in a wall pocket or by anchor shear plate detail. In high seismic areas, the steel frameworks may be designed as moment frames to resist some part of the earthquake loads to provide a second line-of-defense. The most rigorous way of modeling core wall is by the finite element method involving the use of plate and shell elements. However, this approach is computationally intensive for nonlinear analysis because it involves discretization of the wall into a large number of elements. Core wall is characterized by the fact that their cross-sectional and longitudinal dimensions are of different orders of magnitude. The wall thickness is usually small compared with the characteristic cross-sectional dimensions, which in turn are small compared with the height of the core wall. It is proposed that the core wall be modeled as a thin-walled beam-column element (referred as thin-walled element below) for its proportional similarity to Vlasov’s thin-walled beam. The main advantage of such an approach is that the total degrees of freedom of the structure can be reduced tremendously, and the structural behavior can be predicted with sufficient accuracy (Taranath, 1988, 1998; Chen et al., 2000; Liew, 2001b; Liew and Uy, 2001). The fundamental linear theory as well as stability problems of thin-walled members have been treated in the pioneer works by Vlasov (1961) and Timoshenko and Gere (1961). Taranath (1988, 1998) proposed a linear elastic formulation of thin-walled element for the analysis of core-braced frames. A considerable number of works have been presented in the fields of instability of thinwalled beams and frames using various finite element formulations and solution strategies (Barsoum and Gallagher, 1970; Yang and McGuire, 1986a, 1986b; Chan and Kitipornchai, 1987; Chen and Blandford, 1991; Conci, 1992; Izzuddin and Smith, 1996). Although the geometric nonlinear analysis using thin-walled element with asymmetric open cross-sections is well documented in the literature, the derivation of the geometric stiffness matrix appears to be different from one researcher to another based on different assumptions. In Conci (1992), the complete tangent stiffness matrix of a thin-walled element is derived from the virtual work equation based on the UL formulation. The approach includes both doubly symmetric and asymmetric core-wall sections. The centerline of a core wall is located on the shear center axis. Any significant twisting action should be analyzed to include both warping and torsional effects. Material nonlinearity of core walls is considered approximately by using the plastic-hinge formation. Plastic hinges are formed when the cross-sectional forces reach the cross-sectional capacity. A single-story-high core wall is modeled as one thin-walled beam-column element as shown in Figure 6.60a. Figure 6.60c shows a generic thin-walled beam-column element that has an additional warping degree of freedom over the beam-column element at each end. The local coordinate is chosen with axis x lying on the shear center axis, and y and z axes paralleling to the principal y and z axes. The shear center of the core is selected as the reference point so that

220


θ' D θZM

B

VM

a

UM M Floor master node Z

z2

y2 Beam 2 θZD c x2 d

VD

WD D

b

θYD

UD

Beam 1

Floor N

θXD

Y X

Floor L

xK

A Core wall J

a

yK

zK Core wall K

C

y

z

yK

z

θydK θzdK wdK udK θxdK

ZK θ'xdK

vdK d zd

b

yd

uD

D

y0

FyA,uA A

FzA,wA

BA, θ'xA

vD

θzD wD

FxA,uA z0

MxA, θxA

θyD MyB, θyB MzB, θzB

C' FXB,uB

c

B

FyB,vB

MxB, θxB

x

θ'xD XK

MzA, θzA

Centroidal axis

θxD

Cross-section of core wall K

MyA, θyA C

y

Shear centre axis

FXB,wB

BB, θ'xB x

FIGURE 6.60 (a) A building core wall between two floors; (b) deformations of a thin-walled cross section; (c) a generic model for a thin-walled beam-column member.

appropriate transformation matrices can be established to relate the kinematics relationships between the point of contact between beams and columns with the core wall. For example in Figure 6.60b, the displacements at Node d of the core wall may be related to those at the shear center D in the local coordinate. Detailed derivation of the transformation matrices is given in Chen et al. (2000). Material nonlinearity of the core wall is modeled approximately by using the concentrated plastic-hinge approach. The yielding of the core wall section would depend on the combined action of compression, biaxial bending, torsion, and warping. However, in the proposed formulation, the torsional shear and warping effects have been ignored in the plasticity formulation. It is necessary to model these factors if the core wall is subject to significant torsional and warping


221

deformation. Such a situation is best avoided by selecting an appropriate shape and size of the core walls and an appropriate location for lateral load resistance.

6.3.5 Modeling of Composite Semi-rigid End-plate Connection

Composite joints consist of structural steelwork connections, a continuous reinforced slab and a column web panel. The influence of the slab on the steelwork connections and its interaction with the beam and the column increase the complexity of the analysis of composite joints over the bare steel joints. The M-θr response of a composite joint is influenced by the deformation of the connecting plates, bolt deformation and slippage, shear deformation of the column web panel, elongation of steel reinforcement in the slab, and interface slip of shear connectors. To simplify the modeling, a joint can be subdivided into three zones: tension, compression, and shear. Within each zone, the components that contribute to the joint’s response are identified and their loaddeformation characteristic determined. This methodology constitutes the basis of the component method (Anderson, 1999), which has been adopted as a practical approach for predicting the M-θr behavior of steel and composite joints. Because of the nonlinear behavior of various components, evaluation of the M-θr response of steel or composite joints requires an incremental analysis. This approach has been successfully explored by Huber (1999) who developed a computer program to evaluate the M-θr response of composite joints. For design implementation, Eurocode 3 suggests a rotational spring model in which the non-linear M-θr response of joints may be approximated by a bilinear or trilinear rotational joint model. The Eurocode 3 model has been widely accepted for use in the analysis of braced frames in recent years. Tschemmernegg and Huber (1999) used a series of springs to model every component within a composite joint, and they were transformed into a typical rotational spring model by assembling all the component springs. The use of spring elements greatly simplified the complexity of composite joints behavior and allowed direct modeling of joint behavior in analysis of frames. In the modeling of unbraced composite frames, it is necessary to establish a realistic model for beam-to-column composite joints, knowing that these joints behave differently when subjected to positive and negative moment. In Liew et al. (2004), the connection model developed for bare steel joints in Eurocode 3 is extended for composite joints. The methodology covers beam-tocolumn composite joints subjected to both positive and negative moments. It incorporates the effect of slab (concrete and steel reinforcement) and panel zone deformation and their interaction with the steelwork connections. It also explores the option of employing haunched joints in sway and nonsway composite frames by confirming its moment rotational characteristic through tests and to consider the composite action in haunch joint design previously designed as noncomposite. The procedure is validated through comparison with the test results.

6.3.5.1 Moment Resistance

Annex J of Eurocode 3 (CEN, 1992) provides an analytical procedure where the rotational behavior of a joint can be determined by taking into consideration all sources of deformability and resistance within the joint zone (Anderson, 1999). The advantage of this approach is that it can be applied to all types of joints with different configurations by decomposing the joint into relevant components. The M-θr characteristic of a joint can be represented by three properties, namely rotational stiffness, moment capacity, and rotation capacity. The formulae developed from component method for moment capacity and initial rotation stiffness are presented herein.

222


tension Ft

dc 1 Db

h1

Pr1

2 h2

　　 PNA

3

Dwb

Cc

zc

Pr2

compression

FIGURE 6.61 Force diagram in composite flush end-plate connection under negative moment.

6.3.5.1.1 Negative Moment Capacity For composite end-plate connection subject to negative moment, the moment capacity can be determined using plastic analysis of compact steel section with force and stress distribution as shown in Figure 6.61. A similar approach may be used for joint under reversal of loading if panel joint resistance is accounted for when establishing the forces through equilibrium. As long as the compressive and tensile forces of individual components shown in the Figure 6.61 can be determined, the moment capacity of composite joints can be calculated by multiplying these forces with their respective lever arms. The location of Plastic Neutral Axis (PNA) is determined by equating the tensile force contributed by rebar and bolt rows to the compressive resistance. Tests carried out on a composite flush end-plate joint by Liew et al. (2000c) revealed that when the total tensile resistance Fs (inclusive of tensile force contributed by rebar and bolt rows) is larger than the compressive resistance of the bottom beam flange Ffb, PNA is always located above the bottom beam flange and a portion of the beam web Dwb is in compression. Dwb may be determined from force equilibrium as: Fs − Ffb Dwb = 1.2 f yb t wb

(6.63)

It is recommended (SCI/BCSA, 1998) that the yield stress fyb increases by a factor of 1.2 to account for strain hardening when the compression zone is extended into beam web. If only beam flange alone is adequate to resist total tensile resistance, a factor of 1.4 may be used to enhance the yield stress—20 percent each for the beneficial effects of strain hardening and dispersion into the web at the root of the section. The center of compression from the bottom of beam flange Zc may be determined as:

Zc =

2   Dwb   b fb t fb t wb Dwb   + t fb   + 2     2

(6.64)

t wb Dwb + b fb t fb

Taking moment about the center of the compression of all the forces shown in Figure 6.61, the negative moment capacity Mneg may be obtained as (see Figure 6.61):

n    t fb   M neg = Ft ( Db + dc − Z c + ∑  Pri  hi + − Zc   2 i =1     

)

(6.65)


223

Tension Ft

dc 1

db

Pr1

Db

Dh

2 3

PNA Dwb

Cc

thf FIGURE 6.62 Force diagram in composite haunch connection under negative moment.

in which twb is the thickness of beam web, fyb is the yield strength of the beam section, tfb is the thickness of the beam flange, bfb is the width of the beam flange, tfb is the thickness of the beam flange, Ft is tensile force in the effective area of longitudinal reinforcement that stressed to yield strength, Db is the height of the steel beam, dc is the distance from the rebar to the upper beam flange, hi is the distance from bolt rows i to the center of the bottom beam flange, and Pri is the tensile force for the bolt row i. For a composite haunch connection shown in Figure 6.62, the force equilibrium is established by considering the tensile forces contributed by rebar and bolts, and compressive forces contributed by the haunch flange and the web bearing against the column flange. The tests of haunch joints (Liew 2000c) recorded no tensile strain for bolt rows in the haunch indicating that the PNA is above these bolt rows. Examining the compressive resistances of the haunch flange Fhf and haunch web Fhw, it can be shown that:

Fhf < Ft + Pr1 < Fhf + Fhw

(6.66)

Therefore, the PNA lies in haunch web as shown in Figure 6.62 and the depth of haunch web in compression, Dhw may be computed as:

Dhw =

Ft + Pr 1 − Fhf 1.2 f y b thw

(6.67)

The effective compressive resistance Fhw,eff contributed by haunch web, is determined as:

Fhw,eff = 1.2Dhw fybthw

(6.68)

Taking moment about the center of the bottom haunch flange, the moment resistance of the connection may be calculated as:

  D thf  thf  thf  M neg = Ft  Db + dc + Dh −  + Pr 1  D b − d b + Dh −  − Fhw ,eff  hw +  2 2 2    2

(6.69)

in which thf is the thickness of the haunch flange, db is the distance between the first bolt row to the top of upper beam flange, and Dh is the depth of haunch. Other symbols have been defined earlier.

224


Leff

Row 1 alone

Leff

Row 1 & 2 combined

FIGURE 6.63 Equivalent T-stubs.

Mode 2 Bolt failure with flange yielding

Mode 1 Complete flange yielding P1

Q

Q

Q

Mode 3 Bolt failure P2

P3

Q

FIGURE 6.64 Three possible failure modes for column flange or end-plate bending.

6.3.5.1.2 Determination of Potential Bolt Forces Pri An important contribution of the EC model in predicting moment capacity of steel and composite end-plate joints is its ability to quantify the potential bolt force in each row Pri. The bolt resistance may be governed either by the bending of the end plate or column flange or bolt failure, or by tension failure in the beam or column web. The moment capacity is then determined by the coupling tension in the bolt (and reinforcement if it is a composite joint) with compression in the lower part of the beam.


225

For column flange or end-plate bending, the component method in Eurocode converts the complex pattern of yield lines that occur round the bolt into a simple equivalent T-stub as shown in Figure 6.63. The capacity of the T-stub is then checked against three possible failure modes as shown in Figure 6.64. Mode 1, complete flange or end-plate yielding: 4M p P1 = m

Mode 2, bolt failure with flange or end-plate yielding:

P2 =

(

(6.70)

)

2 M p + n ∑ Pt ′ m+n

(6.71)

Pt ′ P3 = ∑

(6.72)

Mode 3, bolt failure: where:

Pi = potential resistance of bolt row or bolt group for mode i Pt ′ = enhanced bolt tension capacity accounted for the prying effect Mp = plastic moment capacity of the equivalent T-stub representing the column flange or end plate:

=

Leff t 2 py

4

(6.73)

Leff = effective length of yield line in equivalent T-stub t = column flange or end-plate thickness

Pr1(col) = [ Row 1 alone ]

Row 1

Row 2 alone

Row 2

Pr2(col) = min

Rows ( 2+1 ) − Pr1

Pr1(beam) = [ Row 1 alone ]

Pr2(beam) = [ Row 2 alone ]

Row 3 Row 3 alone Pr3(col) = min Rows ( 3+2 ) − Pr2 Rows ( 3+2+1 ) − Pr2 − Pr1

Pr3(beam) = min

FIGURE 6.65 Steps in calculating the distribution of bolt forces.

Row 3 alone Rows ( 3+2 ) − Pr2

226


m = distance from bolt center to 20 percent distance into column root or end-plate weld

n = effective edge distance

The potential tensile resistance of a row or a group of bolts due to tension failure in the beam or column web is taken as: Pt = L t t w py

(6.74)

where Lt is the effective length of web assuming a maximum of spread at 60° from the bolts to the center of the web, tw is the web thickness, and py is the design strength of the steel column or beam. Therefore: Pri = min(P1, P2, P3, Pt)

(6.75)

The potential bolt force is calculated one row at one time, starting at the top and working down as illustrated in Figure 6.65. One major improvement to the Eurocode 4 approach is not to restrict the PNA to the center of the bottom beam flange. In the proposed approach, the PNA is allowed to be located in the steel beam web if the steel beam section is compact and when the tensile resistance provided by the rebars and the bolts is higher than the compression resistance of the beam flange. This improvement is demonstrated in Table 6.9 for the test specimens reported by Liew et al. (2004). For the current specimens subjected to reversal moment, the beneficial effect was not obvious, since the majority of joint moment capacities were governed by shear resistance, and therefore the assumption of PNA located at the center of the bottom beam flange is still reasonably accurate. Although the extended end plate that bears against the column flange could contribute marginally to the negative moment capacity, this beneficial effect has been ignored in the proposed calculation procedure. 6.3.5.1.3 Positive Moment Capacity When a composite beam-to-column joint is subject to positive moment, its load transfer mechanisms are different from those subject to negative moment. In this case, the bottom bolt row(s) will be the primary contributor to tensile resistance. Compressive force, which is needed to equilibrate the tensile force, is now formed by the bearing between the concrete slab and the column flanges. The positive moment capacity of the composite joint can be calculated by multiplying the magnitude of the component forces with the respective lever arm. The following assumptions are made: TABLE 6.9 Moment capacity: EC4 model versus the proposed model on negative moment capacity for Phase I specimens

§

Test

Mu,exp (kNm)

EC4 Model Mu,pred (kNm)

Proposed Model Mu,pred (kNm)

SCCB1

271

256

256§

SCCB2

441

298

395

SCCB3

449

298

445

SCCB4

186

130

130§

SCCB5

410

298

395

SCCB6

423

298

395

§

§

PNA located in mid of bottom beam flange in both models


227

1. The bolt-row(s) force that contributes to moment resistance is determined by the same procedures as those for negative moment as described in Section 6.3.5.2. 2. The compression resistance is taken by the bearing force developed between concrete slab and column flange, and the effective bearing width is taken as the width of the column flange. The depth of concrete slab in compression can be determined by comparing the available bolt-row tensile force. The bearing area is then taken as the product of the column flange width and the depth of the concrete slab in compression. This has been confirmed by the test measurement reported in Liew et al. (2000c). When the connection consists of a number of bottom bolt rows, there is a possibility that the upper beam flange is also in compression in order to achieve force equilibrium. Since the slab that bears against the column offers high compression resistance, it is unlikely that the beam web will be in compression. 3. The stress distribution in the concrete slab is assumed to be of a rectangular stress block with a mean stress of 0.85fck or 0.67fcu. 4. The crushing strain of concrete is taken as 0.0035.

Figure 6.66 shows the force diagram of a composite flush end-plate connection subjected to positive moment. If the moment capacity of the composite joint is governed by ductile failure modes such as column flange and end-plate in bending, a plastic stress block distribution may be assumed as shown in Figure 6.66b. On the other hand, the force distribution is assumed to be linear when brittle failure mode is detected, such as the fracture of bolts and column web in tension (Figure 6.66a). The depth of the compression stress block from the top of the slab can be computed based on the equilibrium of forces: c=

Pr 2 + Pr 3 0.85 fck b fc

(6.76)

The moment resistance is then computed by taking moment about the center of the compression stress block as follows:

compression

compression

0.85fck/γM 0.67fcu/γM

PNA

d1 d3 Db

d2

c

dslab

0.85fck/γM 0.67fcu/γM

Fc

c

Fc

1 2 3

Pr2

Pr2

Pr3

Pr3 tension

(a) Linear Distribution FIGURE 6.66 Stress and force distribution under positive moment.

tension

(b) Plastic Distribution

228


(6.77)   c  c M pos = Pr 2  d 2 −  + Pr 3  d3 −  2 2   in which fck is the concrete cylinder compressive strength, bfc is the width of the column flange, and di is the distance between bolt row i to the top of concrete slab. These formulae may be used to calculate positive moment capacity of the haunch joint since the force distribution mechanism is not different from the flush end-plate joint. When establishing the force equilibrium as in Figures 6.61, 6.62, and 6.66, and calculating the moment resistance from Equations 6.65, 6.69, and 6.77, it is assumed that the effective tensile force is equal to or less than the panel zone shear resistance as the compression resistance is not critical for joints subject to reversal loads. 6.3.5.1.2 Panel Zone Shear Resistance When the joints are subjected to reversal of loading, the joint panel zone may deform in shear and the panel zone shear resistance would affect the joint’s moment capacity. Flush end-plate connections SJ1, CJ1, and CJ2 tested by Liew et al. (2000c) show that panel zone failure governed the ultimate capacity. In these test specimens, the column web was not strengthened by doubler plate or concrete encasement. The shear resistance of an unstiffened column web Vwc of a single-sided joint or for a double-sided joint in which the beam depths are similar is determined as: f y ,wc Avc Vwc = β 3

(6.78)

in which Avc = Ac − 2b fc t fc + (t wc + 2rc )t fc is the area of column web, Ac is the cross-section area of the column, bfc is the overall breath of the column, tfc is the thickness of the column flange, twc is the thickness of the column web, rc is the root radius of the column, β is the transformation parameter accounting for the possible influence of the web panel in shear for adjacent connection.

M2

z

θ

z

M1

M2

z

(a)

M2

z

θ

z

M1

z

M1

(b)

z

(c)

θ

M1

M2

z

θ

(d)

FIGURE 6.67 Lever arm z used for joints under reversal of moments: (a) bare steel joint; (b) flush endplate composite joint; (c) haunched composite joint; (d) extended end-plate composite joint.


229

If a doubler plate is used, the shear area may be taken as:

)

Avc ,dp = Ac − 2b fc t fc + ( t wc + 2rc t fc + bs t wc

(6.79)

where bs is the width of the doubler plate. When the steel column web is encased in concrete, the panel shear resistance of the column web may be increased to allow for the encasement: Vwc, con =

)

0.55 ( 0.85 fck Ac ,con sin θ β

(6.80)

 Dc − 2t fc  where Ac,con = 0.8 Dc − 2t fc cos θ (b fc − t wc ) and θ is taken as equal to tan −1   , and z is z   the lever arm as shown Figure 6.67. It was observed from the tests that the presence of concrete slab in a composite joint increased the panel zone shear resistance. This is due to the increase in effective depth of the panel zone compared to that of a steel joint. Larger effective depth would induce smaller panel shear force under the same applied moment. Therefore, less panel zone deformation is expected for composite joints than for steel joints.

(

)

6.3.5.2 Rotational Stiffness

6.3.5.2.1 Rotational Stiffness Under Negative Moment The stiffness model by Anderson (1999) is taken as a basis to determine the initial rotational stiffness of a composite joint. Evaluation of joint elastic stiffness is derived from the elastic translational stiffnesses of the active joint components that form the spring model (Figure 6.68), as: Ez 2 1 ∑k i

Rki =

(6.81)

where:

E = elastic modulus of steel

z = level arm between compressive and tensile areas, or zeq when there is more than one layer of tension, compression, or shear spring

ki = stiffness coefficient of component i, as determined by expressions in Table 6.10

As shown in Figure 6.68, when there is more than one component in a series at the same level r, these components are transformed into keff,r. Similarly, if there are components parallel to the same internal force type (tensile, compression, or shear), the lever arm must be redefined as equivalent lever arm zeq, and subsequently replaced these parallel springs as kEquation. These transformed terms are determined by the expressions:

keff ,r =

zeq

1 1 ∑i k i ,r

∑k = ∑k ∑k r

r

keq =

i

(6.82) h

2 eff ,r r

h h eff ,r r

eff ,r r

zeq

(6.83)

(6.84)

230


k1

θ

k3,1 k4,1 k5,1 k10,1

M2

M2

k3,2 k4,2 k5,2

k10,2

M1

θ

kr

k2

keff,1

keff,1

M1

M2

keff,2

θ

keff,2

M1

k1 k2

k1

θ

M1 k1 k2

k1

M2

k3,1 k4,1 k5,1 k10,1

M2

k3,2 k4,2 k5,2 k10,2

θ

kr=k13kstud

k2

k2

zeq keq

keq zeq

M1

M2

θ

M1

k1 k2

FIGURE 6.68 Spring model for negative and positive moments. TABLE 6.10 Stiffness coefficient (Anderson, 1999; Eurocode 4, 1994) Active components in end plate joint Column web panel in shear

Stiffness Coefficient, ki Without concrete encasement: k1 = With concrete encasement: 0.06

E cm bs hc E βz

Column web in compression Without concrete encasement: k 2 = With concrete encasement: Column web in tension k3 = Column flange in bending k4 = End plate in bending k5 =

0.38Avc βz

0.7beff ,c ,wctwc dc

0.5bel bc E cm hc E

0.7beff ,t ,wctwc dc 0.85leff tfc3 m3 0.85leff t p3 m3 (Continues)


231

TABLE 6.10 (Continued) Beam or column flange and web in compression

k7 = ∞

Beam web in tension

k8 = ∞

Bolts in tension

Slab reinforcement in tension

k10 =

1.6As Lb

For interior joint loaded with gravity load and M1 equal to M2: k13 =

Ar  1+ β  hc  + Kβ   2 

For interior joint subjected to reversal load: k13 =

Ar  1+ β  hc  + Kβ   2 

where Kβ = β (4.3β2 − 8.9β + 7.2) for connection subjected to negative bending; β = 1 connection subjected to positive bending; β = 0 and k13 = 0. Influence of shear stud slip

The influence of shear stud slip on joint stiffness to be imposed on k13 by the reduction factor, kstud to be multiplied to k13. k stud =

ν=

Nk sc 1 and K sc = E r k13  ν − 1  hs 1+ ν − K sc  ν + ξ  ds

(1+ ξ )Nk

l

sc eff ,b

EI

ds2

and ξ =

EI d E s As 2 s

Note: 1. Symbols that are not defined in Table 10 may be referred to (Anderson, 1999; Eurocode 4, 1994) 2. Standard push out test on shear connector were carried out to determine the stiffness, ksc

6.3.5.2.2 Rotational Stiffness Under Positive Moment When a composite connection is subjected to positive moment, it behaves like an inverted steel joint with concrete slab in compression. The lever arm between tension and compression forces is smaller for composite connection under positive moment because the center of compression is located in the concrete slab as compared to the joint under negative moment, as shown in Figure 6.67. Therefore, by using the similar stiffness coefficients as those in the negative model and modified spring model (shown in Figure 6.68), and in Equation 6.81, the initial stiffness under positive moment can be determined.

232


TABLE 6.11 Moment capacity: experimental (Liew et al., 2004) versus analytical results Test

Mu,pred (kNm)

Mu,exp(kNm) Negative

Positive

Negative

Positive

Mu,exp /Mu,pred Negative

Positive

SJ1

125

110

94

94

1.33

1.17

CJ1

268

176

230

147

1.17

1.20

CJ2

273

167

230

154

1.19

1.08

CJ3

339

175

329

143

1.03

1.22

CJ4

318

226

329

195

0.97

1.16

CJ5

568

395

599

339

0.95

1.17

CJ6

632

461

751

429

0.84

1.07

CJ7

372

160

319

147

1.17

1.09

TABLE 6.12 Initial rotational stiffness: experimental (Liew et al., 2004) versus analytical results Test SJ1

Rki,pred (kNm/rad)

Rki,exp (kNm/rad)

Rki,exp/Rki,pred

Negative

Positive

Negative

Positive

Negative

Positive

13103

13091

13944

13944

0.94

0.94

CJ1

28784

17043

27001

15833

1.07

1.08

CJ2

27648

16987

27001

15833

1.02

1.07

CJ3

—

—

42430

24521

—

—

CJ4

42697

45118

42430

41501

1.01

1.09

CJ5

57000

47473

80293

57879

0.71

0.82

CJ6

107790

86737

109908

85550

0.98

1.01

CJ7

39784

23882

36925

20220

1.08

1.18

TABLE 6.13 Initial rotational stiffness: comparison of test results (Liew et al., 2000c) with predicted results for joints under negative moment Test

Rki,exp (kNm/rad)

Rki,pred (kNm/rad)

Rki,exp/Rki,pred

SCCB1

36265

44164

0.82

SCCB2

56328

81271

0.69

SCCB3

83125

122951

0.68

SCCB4

37978

43930

0.86

SCCB5

49678

57670

0.86

SCCB6

50031

58980

0.85

6.3.5.3 Comparison with Test Results

The experimental results presented in Liew et al. (2004) are compared with the analytical predictions in Tables 6.11 and 6.12. The material properties obtained from the coupon tests were used to evaluate the strength and stiffness. Also, the partial safety factors for materials used in the Eurocode 3 and Eurocode 4 formulae are taken as unity. To further verify the accuracy of the analyti-


233

-300 Prediction -200

Moment (kNm)

Negative -100

Test

0 Positive 100 200 300 -0.1

-0.05

0

0.05

0.1

Rotation (rad)

FIGURE 6.69 Comparison of experimental and analytical values for CJ1 (Liew et al., 2004).

cal model, the experimental values of initial rotational stiffness reported by Liew et al. (2004) for joints subject to symmetric loading (i.e., both sides of the beam-to-column connections subject to negative moments) are also compared with the results obtained by the analytical model as shown in Table 6.13. It was observed from Table 6.13 that the EC model slightly over-predicts the initial rotational stiffness for joints loaded in symmetrical load only, but not for joints subject to reversal of loading as shown in Table 6.12. The probable reason is that the deformation behavior of composite joints under reversal of loading are dominated by the panel joint shear deformation, which is well captured by the panel zone model used in the Eurocode code. Figure 6.69 shows the comparison of M-θr curves obtained experimentally with the corresponding analytical curves for CJ1. Bilinear idealization was adopted for the analytical M-θr curves as proposed by Eurocode 3. The comparison of moment capacities in Table 6.10 shows that the analytical method proposed for positive moment capacity is conservative, as the ratio Mu,exp / Mu,pred is always greater than unity. The predicted negative moment capacity for CJ4, CJ5, and CJ6 are higher than the experimental values. This could be explained as the onset of premature failure due to bolt fracture on the connection side loaded with positive bending. Higher moment resistance could be developed if the fracture of the bolt can be avoided. Examination of the ratio of Rki,exp/Rki,pred for positive bending shows good agreement between the predicted values and the experimental results. This indicates that the proposed modification to the EC3 joint model is adequate to provide a safe estimation of the joint’s moment rotational curves. Tables 6.11 shows that the values predicted by the analytical model as proposed by Anderson (1999) are close to the experimental results, except for CJ5 in negative bending. For joints tested under symmetrical loading with negative applied moment, all the initial rotational stiffness obtained analytically exceeded the experimental results. The worst value obtained for the Rki,exp/Rki,pred ratio is 0.68 for specimen SCCB3.

234


Node B Node A Deflection v

First Plastic Hinge Z

Y X

FIGURE 6.70 Formation of plastic hinges in a 20-story composite frame.

In the design of composite frames with semicontinuous joints, it is convenient to represent the overall joint behavior by rotational springs. In an unbraced frame, the joint model should take into account the behavior of the column web panel in shear as well as the M-ϕ behavior of the relevant connection. Liew et al. (2004) provides detailed studies on joints subject to reversal loading leading to a better understanding of the behavior of composite sway frames. The joint model developed can be used in the analysis of composite beams and composite frames.

6.3.6 Analysis of 20-Story Steel Frame with Composite Beams

Figure 6.70 shows a 20-story space frame with composite beams. Properties of steel column and composite beam sections are given in Liew et al. (2001b). A50 steel of yield strength 344.8 N/mm2 is used. The overall slab depth is 127 mm and the cylinder strength of concrete is 27.6 N/mm2. Full shear connection is assumed for the composite beams. The contribution of rebars is assumed to be negligible and therefore ignored in the calculation of the beam capacity. The frame is subject to a combination of gravity loads 4.8 kN/m2 and wind loads 0.96 kN/m2 acting in the Y-direction. Rigid-floor diaphragm action is assumed in the global analysis. Each steel column is modeled using one plastic-hinge beam-column element. Each beam is modeled using four elements. Anal-


1.4

At Node B

1.2

Load Ratio

235

1.0

Limit Load 1.338

1.338 1.031

0.8

1.031 Component Limit State = 0.773

0.6

At Node A

0.4 Inelastic Analysis of Composite Frame Plastic Hinge Analysis of Pure Steel Frame

0.2 0.0 0.000

0.005

0.010

0.015

0.020

0.025

0.030

Top story Deflection v/H in the Y-Direction FIGURE 6.71 Load-deflection curves of the 20-story composite frame.

yses are carried out on the 3-D steel frame and composite frame so that their results can be compared. The load-deflection curves of nodes A and B at the top of the frame are shown in Figure 6.71. The formation of plastic hinges is shown in Figure 6.70. Advanced analysis on the pure steel framework shows that the first plastic hinge occurs at a load ratio of 0.784 and the limit load of the frame is reached at 1.031. At the limit load, most plastic hinges occur in the beams on the right side of the frame. In the analysis of a composite frame, the composite action between the steel beams and concrete slab is fully accounted, and the composite beams are analyzed using an inelastic approach based on the moment-curvature relationship given in Section 6.3.3. The frame collapses at a load ratio of 1.338, which represents a 30 percent increase of limiting strength compared with the pure steel frame. The component limit-state check approach predicts a limit load of 0.773. The analysis is based on a second-order elastic analysis, and the limit load is similar to the load ratio of the first plastic hinge occurring in the steel frame. This is because the beam end is subject to hogging moment and behaves like a pure-steel section. The strength increase of the composite frame due to the inelastic force redistribution beyond the first member nominal strength is 73 percent. Due to higher redundancy in large frameworks, the strength increase of the 20-story frame considering the composite action is much higher than that of the small-scale frame. In the analysis of 20-story frame with composite beams, Liew et al. (2001b) found that computing the elastic serviceability deflections for predominant lateral load using the averaged inertia of composite beam section:

I c = 0.4 I + 0.6 I ′

(6.85)

is more accurate than that using the following equation (Viest et al. 1997):

I c = 0.6 I + 0.4 I ′

(6.86)

in which I and Iʹ are the moment of inertia of the composite beam section under the positive moment and negative moment respectively. This finding is consistent with the experimental evidence by Di Sarno and Elnashai (2002).

236


Core

Wind Load 24 x 3.658m = 87.792m

Z Y m

15

7.3

m

15

7.3

5m

1 7.3

7.3

Y

96

m

15

7.3

m

6.0

96

m

96

m

1

2

Lintel beam

W16 x 45

W16 x 45

W16 x 45

W14 x 30

W14 x 30

W14 x 30

W14 x 30

7,315m

7,315m

7,315m

7,315m

3

FIGURE 6.72 Multistory frame with strong core.

4

5

W14 x 34

W16 x 45

W14 x 34

W14 x 34

W16 x 45

W14 x 34

W14 x 34

W14 x 34

W14 x 34

7,315m

W16 x 45

W14 x 30

W14 x 34

W14 x 30

Thickness of wall = 406mm

W14 x 30

W14 x 34

Connection

W14 x 30

W14 x 34

W16 x 45

W14 x 34

W14 x 34 W14 x 34

A

W16 x 45

W14 x 30

W14 x 34

6,096m

B

W14 x 34

6,096m 6,096m

C

6.0

6.0

1,829m 3,658m 1,829m W14 x 30

D

m 15

W14 x 34

X

6

X

237

24 x 3.658 m = 87.792 m


Wind load

z y x

m 7.3

m 15

5m

1

7.3

8.5

34

5m

1 7.3

y 1.829 m

m

W14x34

W14x30

W14x30

Thickness of wall = 254 mm

W16x45

W16x45

W16x45

W14x30

W14x30

7.315 m 2

Lintel beam

W14x30

7.315 m 3

FIGURE 6.73 Multistory frame with weak core.

W18x60

W18x60

Connection

W14x30

7.315 m 4

W18x60

W16x45

W18x60

W16x45

W18x60

W16x45

W12x16

W16x45

7.315 m 1

m

96

m

W16x45

W14x30

A

58

1.829 m

W14x30 W14x34

W14x30 W14x34

W14x34 W12x16

6.096 m 8.534 m

B

W18x60

C

3.658 m

D

W14x30

3.658 m

6.0

3.6

W12x16

15

7.3

W14x34

m

W14x34

15

7.3

x

7.315 m 5

6

238


6.3.7 Analysis of Core-braced Multistory Frame

Figures 6.72 and 6.73 show the plan and isometric views of a 24-story core-braced frame with strong and weak core walls, respectively. The total height of the building frame is about 88 m. The wall thickness of the strong core is 406 mm, and the weak core-wall is 254 mm. Concrete lintel beams with a depth of 1.219 m are rigidly connected to the two C-shaped core-wall sections to enhance its resistance against torsion. All steel members are A36 steel. All floor plates are assumed to be rigid in plane to account for the diaphragm action of concrete slabs. The elastic modulus of concrete is 23,400 N/mm2, and the compressive strength of concrete is 23.4 N/mm2. The structure is analyzed for the most critical load combination of gravity loads, 4.8 kN/m2, and wind loads, 0.96 kN/m2, acting in the Y direction. Each steel column is modeled as one plastic-hinge beam-column element, and each beam as four plastic-hinge beam-column elements. The core-wall section is modeled using two C-shaped sections interconnected by lintel beams. Each C-shape core wall is modeled using one thin-walled element within a story height. The floor beams are assumed to be connected to the center dimensions of the concrete core wall. The finite width (thickness) of the core is not modeled in the analysis. This is because the half thickness of the core wall is only 128 mm, which is about 2 percent of the beam length. For this particular problem, the effect of finite wall thickness will not affect the computed results significantly. However, if the wall thickness is significant compared to the beam length, the finite thickness of the core wall may be modeled using a rigid link element to reflect the real behavior of a core-braced frame. The plastic moment resistance of the core-wall section has been reduced to approximately account for the tensile cracking; they are 1.57 × 105 kNm for the strong core and 4.8 × 104 kNm for the weak core wall.

6.3.7.1 Core-braced Frames with Strong Core Walls

Inelastic analyses are first carried out on the core-braced frame with strong core walls. If the steel frameworks are pin-connected to the concrete core, the whole building relies on the core to provide the lateral resistance. The system reaches its limit of resistance at a load ratio of 2.082 when a plastic hinge forms at the bottom of the core walls as shown in Figure 6.74a. If the presence of the core wall is ignored, the unbraced rigid frame can provide lateral load resistance up to a load ratio of 0.539 as shown in Figure 6.74a. The limit load of the unbraced rigid framework is about 26 percent of the limit load of the central core walls. In the case of a strong core, the lateral load resistance of the core wall is higher than that of the rigid frameworks. To study the connection effects in core-braced frames, inelastic

Load Ratio

2.5

2.454

0.77

0.0 0.000

0.005

1.156

0.77

DWA

0.0 0.000

0.015

b

TSAW

0.654

0.5

0.010

1.660 EEP

1.023

Core-braced frame Unbraced rigid frameworks

Top storey deflection in the Y-direction, v/H

Limit load 1.787

1.311

1.0

0.539

H/400

Rigid First hinges in core-walls, 1.527

1.5

TSAW

Pinned connection

1.5 1.0

EEP 2.303

DWA

0.5

a

2.254 2.128 2.082

2.0

2.0

Limit load 2.633 2.552

First hinges in Rigid core-walls, 2.567

Load Ratio

3.0

Pinned connection

Core-braced frame Unbraced rigid frameworks

H/400

0.005

0.684 0.641

0.010

0.015

0.020

Top storey deflection in the Y-direction, v/H

FIGURE 6.74 Nonlinear inelastic analysis of core-braced frames (a) frame with strong core walls; (b) frame with weak core walls.

1.03 0.94 1.05 0.97

1.04 1.06 1.06

Top and seat angle connection with double web angles

Top and seat angle connection

Extended end plate connection without column stiffeners

Extended end plate connection with column stiffeners

Flush end plate connection without column stiffeners

Flush end plate connection with column stiffeners


DWA

TSAW

TSA

EEP

EEPS

FEP

FEPS

HP

142

314

218

221

309

448

363

301

110

Rki′ = Rkj M n

13.2

4.5

3.6

2.2

5.5

7.3

6.9

5.0

10.6

Rkp ′ = Rkp M n

Note: Mpb = the plastic capacity of the beam where the semi-rigid connection is located

0.91

0.98

Double web angle connection

M 0′ = M 0 M n

Single web angle connection

Connection name

SWA

Connection type

TABLE 6.14 Parameters and values of Mn /Mpb for connections subjected to in-plane bending

1.20

1.03

1.23

1.42

1.20

0.80

1.11

1.06

1.44

n

0.078

0.429

0.378

1.371

1.040

0.302

0.467

0.053

0.023

At the beam framing about the major axis of column

0.039

0.214

0.189

0.680

0.520

0.151

0.233

0.026

0.011

At the beam framing about the minor axis of column

Mn/Mpb

Advanced Analysis of Steel and Composite Semi-rigid Frames 239

240


TABLE 6.15 Comparison of limit loads and elastic lateral stiffness of core-braced frames with strong core walls Connection types DWA (Double web angle connection)

Limit load

Initial lateral stiffness

102%

104%

TSAW (Top and seat angle connection with double web angles)

111%

131%

EEP (Extended end plate without column stiffener)

123%

154%

Rigid connection

126%

185%

*All % values are compared with the core-braced frame with pinned connections

analyses are carried out for core-braced frames with DWA, TSAW, EEP, and rigid connections. The properties of DWA, TSAW, and EEP connections are given in Table 6.14. The four-parameters of the power model for semi-rigid connections are evaluated based on the statistic values obtained from the connection test database, so there is no need to know the connection details in order to perform the analysis (Hsieh and Deierlein, 1991). As shown in Table 6.15, the limit load and elastic lateral stiffness of core-braced frame with DWA connections are respectively 1.02 times and 1.04 times those of the core-braced frame with pinned connections. The use of DWA connections does not increase the limit load and lateral stiffness significantly. If TSAW, EEP, and rigid connections are used, the surrounding frameworks will provide additional resistance to lateral loads, and the limit loads are increased by 11 percent, 23 percent, and 26 percent, respectively. Because the core-braced frame relies mainly on the strong core walls to provide lateral resistance, the frames collapse soon after the cross-section capacity of the core wall is reached. It is also found that the lateral stiffness of the building can be enhanced by 31 percent and 54 percent if TSAW and EEP connections are used (see Table 6.15). Serviceability checks are also performed on the core-braced frames. All the floor beams satisfy the deflection requirement of span/360 under the service live load. It is observed from Figure 6.74a that the core-braced frames with strong core walls satisfies the lateral drift requirement, (story height)/400, for service wind load. Hence, several connections can be used if strong core walls are used for lateral load resistance. Since the pinned connection is the cheapest for construction, they are preferred for frames braced by the strong core walls.

6.3.7.2 Core-braced Frames with Weak Core Walls

Nonlinear analyses are also carried out on core-braced frames with weak core walls. Core-braced frames with pinned connections collapse at a load ratio of 0.641 as shown in Figure 6.74b. The TABLE 6.16 Comparison of limit loads and elastic lateral stiffness of core-braced frames with weak core walls Connection types DWA (Double web angle connection)

Limit load

Initial lateral stiffness

107%

120%

TSAW (Top and seat angle connection with double web angles)

180%

306%

EEP (Extended end plate without column stiffener)

259%

440%

Rigid connection

279%

571%

*All % values are compared with the core-braced frame with pinned connections


241

limit load of the pure steel frameworks is 0.654, which is 2 percent higher than that of the corebraced frame with pinned connections. The elastic lateral stiffness of steel frameworks is 40 percent higher than that of the RC core. Inelastic analyses are carried out for core-braced frames with DWA, TSAW, EEP, and rigid connections. It is found that the use of DWA connections does not increase the limit load and lateral stiffness of core-braced frames significantly. If TSAW, EEP, and rigid connections are used, first hinges will form in the core walls at much higher load ratios. The frames have much strength reserve beyond the first plastic hinge, and the limit loads are respectively 1.8, 2.59, and 2.79 times those of the core-braced frame with pinned connections. It is found that the lateral stiffness can be respectively enhanced to 3.06, 4.4, and 5.71 times those of a core-braced frame with pinned connections if TSAW, EEP, and rigid connections are used (see Table 6.16). This is because the steel frameworks are much stiffer and stronger than the weak core. For core-braced frames with weak core walls, the strength and stiffness increase due to the use of semi-rigid connections is much more significant than core-braced frames with strong core walls. The combined use of core wall and rigid frame satisfies the deflection-limit requirement for lateral drift. But the core wall, when used together with other semi-rigid frames, does not satisfy the lateral drift requirement. It can be concluded from the study that if a weak core design is adopted, it is necessary to provide proper connection detailing in order to satisfy the requirements for strength and serviceability limit states.

6.3.7.3 Second-order Effects in the Core-braced Frame

If first-order elastic analyses are carried out on the strong core frame where the connections are designed as pin joints, the frame reaches a limit load ratio of 2.213 based on the plastic capacity check on the core wall section. From the second-order inelastic analysis, first plastic hinge forms at the base of core walls at a load ratio of 2.082. Since the surrounding steel framework relies on the building core to provide lateral stability, the limit load is reduced by 9 percent and the lateral deflection is increased by 10 percent due to the lean column effect and the second-order effect due to the cantilever action of the concrete core. For the core-braced frame with a weak core, the second-order effects also reduce the limit load by 9 percent and increase the lateral deflection by 10 percent. Hence, it is important to account for the geometrical nonlinear effects in the analysis of core-braced frames. It is noted that a coarse inelastic model is adopted for core wall in the present analysis. Computers and Structures of Berkeley, California, has implemented a section designer in its integrated building design software, ETABS (Version 8, 2002). This section designer is able to predict the section capacity and moment-curvature curve of a concrete core-wall section under the combined action of axial force and biaxial mending moment. Similar developments can be found in El-Tawil et al. (1995). More research needs to be carried out to incorporate these features and to study the influence of axial load-moment interaction and core-wall ductility on the ultimate load capacity of core-braced frames.

References Abdel-Ghaffar, M., White, D. W., and Chen, W. F., Simplified second-order inelastic analysis for steel frame design. Special Volume of Session on Approximate Methods and Verification Procedures of Structural Analysis and Design, Proc. at Structures Congress 91, New York, ASCE, 47–52, 1991. AISC, Load and Resistance Factor Design Specification for Structural Steel Buildings, American Institute of Steel Construction, 2nd Ed., Chicago, IL, 1993. AISC, Load and Resistance Factor Specification for Structural Steel Buildings, American Institute of Steel Construction, 3rd Ed, Chicago, IL, 2001. AISC, Specification for Structural Steel Buildings, March 9, 2005, ANSI/AISC 360–05, 2005.

242


Alemdar, B. N. and White, D. W., Displacement, flexibility, and mixed beam-column finite element formulations for distributed plasticity analysis, Journal of Structural Engineering, ASCE, 131(12), 1811–1819, 2005. Al-Bermani, F. G. A. and Kitipornchai, S., Nonlinear analysis of thin-walled structures using least element/ member, Journal of Structural Engineering, ASCE, 116(1), 215–234, 1990. Al-Bermani, F. G. A. and Kitipornchai, S., Nonlinear analysis of transmission towers, Engineering Structures, 14(3), 139–151, 1992. Al-Bermani, F. G. A., Zhu, K., and Kitipornchai, S., Bounding-surface plasticity for nonlinear analysis of space structures, International Journal for Numerical Methods in Engineering, 38(5), 797–808, 1995. Amdahl, J., Johansen, A., and Svanø, G., Ultimate capacity of jack-ups considering foundation behaviour, Proc. 7th International Conference on the Behaviour of Offshore Structures, BOSS’94, Boston, USA, 1994. Anderson, D., Composite steel-concrete joints in frames for buildings: design provision, COST C1 Document; 1999. Ang, K. M. and Morris, G. A., Analysis of three-dimensional frames with flexible beam-column connections, Canadian Journal of Civil Engineering, 11, 245–254, 1984. API RP 2A-WSD, Recommended practice for planning, designing and constructing fixed offshore platforms— Working stress design, American Petroleum Institute, 2002. AS4100, Steel Structures, Standards Australia, Sydney, 1990. Attalla, M. R., Deierlein, G. G., and McGuire, W., Spread of plasticity: quasi-plastic-hinge approach, Journal of Structural Engineering, ASCE, 120(8), 2451–2473, 1994. Attalla, M. R., Deierlein, G. G., and McGuire, W., Nonlinear frame analysis with torsional-flexural member behaviour. In: Proceedings of the Fifth International Colloq. On Stability and Metal Structures, SSRC, Lehigh University, 11–19, 1996. Attiogbe, G. and Morris, G., Moment-rotation functions for steel connections, Journal of Structural Engineering, ASCE, 117(6), 1703–1718, 1991. Avery, P. and Mahendran, M., Distributed plasticity analysis of steel frame structures comprising non-compact sections, Engineering Structures, 22, 901–919, 2000a. Avery, P. and Mahendran, M., Refined plastic hinge analysis of steel frame structures comprising noncompact sections I: Formulation, Advances in Structural Engineering, 3(4), 291–307, 2000b. Bailey, C. G., Burgess, I. W., and Plank, R. J., Analysis of the effects of cooling and fire spread on steel-concreteframed buildings, Fire Safety Journal, 26, 273–293, 1996. Bathe, K. J. and Bolourchi, S., Large displacement analysis of three-dimensional beam structures, International Journal for Numerical Methods in Engineering, 14, 961–986, 1979. Barsoum, R. S. and Gallagher, R. H., Finite element analysis of torsional flexural stability problems, International Journal for Numerical Methods in Engineering, 2, 335–352, 1970. Bjorhovde, R., Brozzetti, J., and Colson, A. (eds.), Connections in steel structures: Behaviour, strength and design, Proceedings of the Workshop on Connections held at the Ecole Normale Superiere, Cachan, France, May 1987, Elsevier Applied Science, London, 1988. Bjorhovde, R., Brozzetti, R.J., and Colsen, A., A classification system for beam-to-column connections, Journal of Structural Engineering, ASCE, 116(ST11), 3059–3076, 1990. Bjorhovde, R., Colson, A., Haaijer, G., and Stark, J. W. B. (eds.), Connections in steel structures II: behaviour, strength and design, Pittsburgh, April, 1991, AISC, Chicago, 1992. Bjorhovde, R., Colson, A., and Zandonini, R. (eds.), Connections in steel structures III: Behaviour, strength and design, Proceedings of the Third International Workshop on Connections, Trento, Italy, May, 1995, Pergamon Press, London, 1996. Blandford, G. E., Review of progressive failure analyses for truss structures, Journal of Structural Engineering, ASCE, 123(2), 122–129, 1997. Bolt, H. M., Billington, C. J., and Ward, J. K., Results from large scale ultimate load tests on tubular jacket frame structures, Offshore Technology Conference, OTC 7451, 1994. Bolt, H. M. and Billington, C. J., Results from ultimate load tests on 3-D jacket-type structures, Proc. of Offshore Technology Conference, OTC11941, Houston, Texas, USA, May 2000.


243

Bomel Limited, Analytical and experimental investigation of the behavior of tubular frames, Phase II. Part 4: Summary and Conclusions from Phase I and Phase II, Joint Industry Funded Research Programme, 1992. Bozzo, E. and Gambarrotta, L., Inelastic analysis of steel frames for multistory buildings, Computers and Structures, 20(4), 707–713, 1985. Bradford, M. A., Local buckling analysis of composite beams, Civil Engineering Transactions, Institution of Engineers, Australia, CE28(4), 312–317, 1986. Bradford, M. A. and Gao, Z., Distortional buckling solutions for continuous composite beams, Journal of Structural Engineering, ASCE, 118(1), 73–89, 1992. BS5400, Steel, concrete and composite bridges: Part 5: Code of practice for design of composite bridges, London: British Standards Institution, 1979. BS5950-1, Structural use for steelwork in building, Code of practice for design-rolled and welded sections, British Standards Institution, 2000. Bursi, O. S. and Jaspart, J. P., Benchmarks for finite element modelling of bolted steel connections, Journal of Constructional Steel Research, 43(1–3),17–42, 1997. Buitrago, J., Healy, B. E., and Chang, T. Y., Local joint flexibility of tubular joints, Proceedings of Offshore Mechanics and Arctic Engineering Conference, ASME, 1, 405–411, 1993. CEN, Eurocode 3, Design of Steel Structures, Part 1.1: General Rules and Rules for Buildings, ENV 1993-1-1: 1992, European Committee for Standardization, Brussels, Belgium, 1992. CEN, Eurocode 3, Design of Steel Structures, Part 1.2: General Rules Structural Fire Design, ENV 1993-1-2: 2001, European Committee for Standardization, Brussels, 2001. CEN, Eurocode 4, Design of Composite Steel and Concrete Structures, Part 1.1: General Rules and Rules for Buildings, ENV 1994-1-1, London, British Standards Institution, 1994. Chajes, A. and Churchill, J. E., Nonlinear frame analysis by finite element method, Journal of Structural Engineering, ASCE, 113, 1221–1235, 1987. Chan, S. L. and Kitipornchai, S., Geometric nonlinear analysis of asymmetric thin-walled beam-columns, Engineering Structures, 9(4), 243–254, 1987. Chan, S. L. and Zhou, Z. H., Second-order elastic analysis of frames using single imperfect element per member, Journal of Structural Engineering, ASCE, 121(6):939–945, 1995. Chan, S. L. and Gu, J. X., Exact tangent stiffness for imperfect beam-column members, Journal of Structural Engineering, ASCE, 126(9), 1094–1102, 2000. Chan, S. L. and Gu, J. X., Exact tangent stiffness for imperfect beam-column members—Closure, Journal of Structural Engineering, ASCE, 127(12), 1492–1494, 2001. Chan, S. L., Review: Non-linear behavior and design of steel structures, Journal of Constructional Steel Research, 57, 1217–1231, 2001. Chan, S. L. and Chan, B. H. M., Refined plastic hinge analysis of steel frames under fire, Steel and Composite Structures, 1(1), 111–130, 2001. Chan, S. L., Shu, G. P., and Lü Z. T., Stability analysis and parameter study of pre-stressed stayed columns, Engineering Structures, 24, 115–124, 2002. Chan, S. L. and Zhou, Z. H., Elastoplastic and large deflection analysis of steel frames by one element per member. II: three hinges along member, Journal of Structural Engineering, ASCE, 130(4), 545–553, 2004. Chen, B., Hu, Y., and Tan, M., Local joint flexibility of tubular joints of offshore structures, Proceedings of Offshore Mechanics and Arctic Engineering Conference, OMAE, Houston, Texas, 1990. Chen, H. and Blandford, G. E., Thin-walled space frames, Parts I and II, Journal of Structural Engineering, ASCE, 117(8), 2499–2539, 1991. Chen, H., Nonlinear inelastic analysis of steel-concrete composite frames, Thesis presented to National University of Singapore, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Singapore, 2000. Chen, H., Liew, J. Y. R., and Shanmugam, N. E., Nonlinear inelastic analysis of building frames with thinwalled cores, Thin-Walled Structure, 37(3), 189–205, 2000. Chen, H. and Liew, J. Y. R., Explosion and fire analysis of steel frames using mixed element method, Journal of Engineering Mechanics, ASCE, 131(6), 606–616, 2005.

244


Chen, W. F. and Atsuta, T., Theory of beam-column. Vol. 1, Inplane behaviour and design, McGraw-Hill, New York, 1976. Chen, W. F. and Atsuta T., Theory of beam-column. Vol. 2, Space behaviour and design, McGraw-Hill, New York, 1977. Chen, W. F. and Lui, E., Stability design of steel frames, CRC Press, Boca Raton, FL, 1991. Chen, W. F. and Toma, S., Advanced analysis of steel frames: Theory, software, and applications. CRC Press, Boca Raton, FL, 1994. Chen, W. F., Goto, Y., and Liew, J. Y. R., Stability design of semi-rigid frames, John Wiley & Sons Inc., New York, 1996. Chen, W. F. and Kim, S.E., LRFD steel design using advanced analysis. CRC Press, Boca Raton, FL, 1997 Chen, W. F., Structural stability: from theory to practice, Engineering Structures, 22, 116–122, 2000. Chen, W. F., Structural Engineering: seeing the big picture, KSCE Journal of Civil Engineering, 12(1), 25–29, 2008. Choo, Y. S., Qian, X. D., and Foo, K. S., Nonlinear analysis of tubular space frame incorporating joint stiffness and strength, 10th International Jack-Up Platform Conference, 13-14. Sept. London, 2005. Clarke, M. J., Plastic zone analysis of frames, in advanced analysis of steel frames: Theory, software, and applications, Chen, W. F. and Toma, S. eds., CRC Press, Boca Raton, FL., 259–319, 1994. Conci, A., Large displacement analysis of thin-walled beams with generic open section, International Journal for Numerical Methods in Engineering, 33, 2109–27, 1992. Crues, G. J., Torres, P. L., and Groehs, A. G., Elastoplastic frame analysis with generalized yield function and finite displacements, Computers and Structures, 18(5), 925–929, 1984. Da Silva, L. S., Towards a consistent design approach for steel joints under generalized loading, Journal of Constructional Steel Research, 64, 1059–1075, 2008. Dai, Y. J., The effect of joint performance on global behaviour of tubular steel structures, Engineering thesis, Dept of Civil Engineering, National University of Singapore, Singapore, 2002. Deierlein, G. G., Zhao, Y., and McGuire, W., A two-surface concentrated plasticity model for analysis of 3-D framed structures, Annual Tech. Session Proc., SSRC, April 15–17, Chicago, IL, 423–432, 1991. Di Sarno, L. and Elnashai, A.S., Seismic retrofitting of steel and composite building structures, Report No. 0201, Mid-America Earthquake Center, Civil and Environmental Engineering Deptartment, University of Illinois at Urbana-Champaign, 2002. Diedricks, A. A., Uy, B., Bradford, M. A., and Oehlers, D. J., Mixed analysis approach for semi-continuous steel-concrete composite beams under uniform loading, Proceedings of Composite Construction in Steel and Concrete IV Conference, May 29–June 2, 2000, Banff, Alberta, Canada, 2000. DNV-RP-C204, Det Norske Veritas Recommended Practice—Design Against Accidental Loads, Nov., 2004. Duan, L. and Chen, W. F., A yield surface equation for doubly symmetric sections, Engineering Structures, 12(2), 114–119, 1990. El-Rimawi, J. A., Burgess, I. W., and Plank, R. J., The analysis of semi-rigid frames in fire—a secant approach, Journal of Constructional Steel Research, 22, 125–146, 1995. El-Tawil, S., Sanz-Picon, C. F., and Deierlein, G. G., Evaluation of ACI 318 and AISC (LRFD) strength provisions for composite beam columns, Journal of Constructional Steel Research, 34, 103–123, 1995. El-Tawil, S. and Deierlein, G. G., Stress-resultant plasticity for frame structures, Journal of Engineering Mechanics, ASCE, 24(12), 1360–1370, 1998. El-Tawil, S. and Deierlein, G. G., Nonlinear analysis of mixed steel-concrete frames. Parts I: Element formulation, Part II: Implementation and verification, Journal of Structural Engineering, ASCE, 127(6), 647–665, 2001. ETABS Version 8, Integrated building design software—Section designer manual, Computers and Structures, Berkeley, California, USA, 2002. Faella, C., Piluso, V., and Rizzano, G., Structural steel semirigid connections: Theory, design and software. CRC Press, Boca Raton, 2000. Fang, L. X., Chan, S. L., and Wong, Y. L., Strength analysis of semi-rigid steel concrete composite frames, Journal of Constructional Steel Research, 52, 269–291, 1999. Fang, L. X., Chan, S. L., and Wong, Y. L., Numerical analysis of composite frames with partial shear-stud interaction by one element per member, Engineering Structures, 22, 1285–1300, 2000.


245

Fessler, H., Mockford, P. B., and Webster, J. J., Parametric equations for the flexibility matrices of single brace tubular joints in offshore structures, Proceedings of the Institution of Civil Engineers, London, ICE, 2, 659–673, 1986a. Fessler, H., Mockford, P. B., and Webster, J. J., Parametric equations for the flexibility matrices of multi-brace tubular joints in offshore structures, Proceedings of the Institution of Civil Engineers, London, ICE, 2, 675–696, 1986b. Gattass, M. and Abel, J. F., Convected systems for curved structural elements, International Journal for Numerical Methods in Engineering, 24, 2143–2166, 1987a. Gattass, M. and Abel, J. F., Equilibrium considerations of the updated lagrangian formulation of beamcolumns with natural concepts, International Journal for Numerical Methods in Engineering, 24, 2119– 2141, 1987b. Goverdhan, A. V., A collection of experimental moment-rotation curves and evaluation of prediction equations for semi-rigid connections, Thesis presented to Vanderbilt University, in partial fulfillment of the requirements for the degree of Master of Science, Nashville, TN, 1983. Hajjar, J. F. and Gourley, B. C., A cyclic nonlinear model for concrete-filled tubes. I: Formulation, Journal of Structural Engineering, ASCE, 123(6), 736–744, 1997. Hajjar, J. F., Evolution of stress-resultant loading and ultimate strength surfaces in cyclic plasticity of steel wide-flange cross-sections, Journal of Constructional Steel Research, 59, 713–750, 2003. Hellan, Ø., Nonlinear pushover and cyclic analysis in ultimate limit state design and re-assessment of tubular steel offshore structures, Thesis presented to the Norwegian Institute of Technology, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Norway, 1995. Himly, S. I. and Abel, J. F, Material and geometric nonlinear dynamics analysis of steel frames using computer graphics, Computers and Structures, 21(4), 825–840, 1985. Hodge, P. G., Automatic piecewise linearization in ideal plasticity, Computer Methods in Applied Mechanics and Engineering, 10, 249–272, 1977. Hsieh, S. H. and Deierlein, G. G., Nonlinear analysis of three-dimensional frames with semi-rigid connections, Computers and Structures, 41(5), 995–1009, 1991. Huber, G., Nonlinear calculations of composite sections and semi-continuous joints, Thesis presented to University of Innsbruck, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Innsbruck, Austria, 1999. Iyengar, S. H., Mixed steel-concrete high-rise systems. In: Sabnis GM, editor. Handbook of composite construction engineering, Chapter 7, Van Nostrand Reinhold Company, New York, 1979. Iyengar, S. H., Baker, W. F., and Sinn, R., Multi-storey buildings, in Chapter 6.2, Constructional Steel Design, An International Guide, Dowling, P. J., Harding, J. E. and Bjorhovde (eds), R., Elsevier Applied Science, London and New York, 1992. Izzuddin, B. A. and Elnashai, A. S., Adaptive space frame analysis, Part I: A plastic hinge approach, Part II: A distributed plasticity approach, Proc Instn Civ Engrs Structs & Bldgs, 99, 303–326, 1993a. Izzuddin, B. A. and Elnashai, A. S., Eulerian formulation for large-displacement analysis of space frames, Journal of Engineering Mechanics, ASCE, 119(3), 549–569, 1993b. Izzuddin, B. A. and Smith, D. L., Large displacement analysis of elastoplastic thin-walled frames. I: formulation and implementation, Journal of Structural Engineering, ASCE, 122(8), 905–914, 1996. Izzuddin, B. A., Conceptual issues in geometrically nonlinear analysis of 3-D framed structures, Computer Methods in Applied Mechanics and Engineering, 191, 1029–1053, 2002. Jiang, X. M., Chen, H., and Liew, J. Y. R., Spread-of-plasticity analysis of three-dimensional steel frames, Journal of Constructional Steel Research, 58, 193–212, 2002. Johnson, R. P. and Bradford, M. A., Distortional lateral buckling of continuous composite bridge girders, In Morris, L. J. (ed.) International Conference on Stability and Plastic Collapse of Steel Structures, Granada, 569–580, 1983. Kamba, T., Prediction equation for initial stiffness and ultimate capacity of unstiffened CHS column and H-beam connections, Doc For Tubular Structure Committee of the AIJ, 1997. (Japanese) Kassimali, A. and Abbasnia, R., Large deformation analysis of elastic space frames. Journal of Structural Engineering, ASCE, 117(7), 2069–2087, 1991.

246


Kemp, A. R. and Nethercot, D. A., Required and available rotations in continuous composite beams with semi-rigid connections, Journal of Constructional Steel Research, 57(1–3), 375–400, 2001. Kim, S. E., Park, M. H., and Choi, S. H., Direct design of three-dimensional frames using practical advanced analysis, Engineering Structures, 23, 1491–1502, 2001. King, W. S., White, D. W., and Chen, W. F., Second-order inelastic analysis methods for steel-frame design, Journal of Structural Engineering, ASCE, 118(2), 408–428, 1992. Kishi, N. and Chen, W. F., Data base of steel beam–to–column connections, Vol. 1 & 2, Structural Engineering Report No. CE-STR-86-26, School of Civil Engineering, Purdue University, West Lafayette, IN, 1986. Kishi, N., Chen, W. F., Goto, Y., and Matsuoka, K., Design aid of semi-rigid connections for frame design, AISC Engineering Journal, 30(3), 90–107, 1993. Kishi, N., Komuro, M., and Chen, W. F., Four-parameter power model for M-θr curves of end-plate connections. Proceedings of Connections in Steel Structures V: Behaviour, Strength and Design, Amsterdam, Netherlands June 3–4, 2004. Kitipornchai, S., Zhu, K., Xiang, Y., and Al-Bermani, F. G. A., Single-equation yield surface for monosymmetric and asymmetric sections, Engineering Structures, 13, 366–370, 1991 Kitipornchai, S. and Al-Bermani, F. G. A., Nonlinear analysis of lattice structures, Journal of Constructional Steel Research, 23(1–3), 209–225, 1992. Komuro, M., Kishi, N., and Chen, W. F., Elasto-plastic FE analysis on moment-rotation relations of top- and seat-angle connections, Proceedings of Connections in Steel Structures V: Behaviour, Strength and Design, Amsterdam, Netherlands June 3–4, 2004. Kondoh, K. and Atluri, S. N., A simplified finite element method for large deformation, post-buckling analysis of large frame structures, using explicitly derived tangent stiffness matrices, International Journal for Numerical Methods in Engineering, 23, 69–90, 1986. Krenk, S., Vissing-Jørgensen, C., and Thesbjerg, L., Efficient collapse analysis techniques for framed structures, Computers and Structures, 72, 481–496, 1999. Krishnamurthy, N. and Graddy, D. E., Correlation between 2- and 3-dimensional finite element analysis of steel bolted end-plate connections, Computers and Structures, 6, 381–389, 1976. Kuo, S. R., Yang, Y. B., and Chou, J. H., Nonlinear analysis of space frames with finite rotations, Journal of Structural Engineering, ASCE, 119(1), 1–15, 1993. Landesmann, A., Batista, E. D. M, and Alves, J. L. D., Implementation of advanced analysis method for steelframed structures under fire conditions, Fire Safety Journal, 40, 339–366, 2005. Leon, R. T., Hoffman, J., and Staeger, T., Design of partially–restrained composite connections, AISC Design Guide 8, American Institute of Steel Construction, Chicago, 1996. Leon, R. T., Design guide for partially retrained composite connections, Journal of Structural Engineering, ASCE, 124(10), 1099–1114, 1998. Leu, L. J. and Tsou, C. H., Second-order analysis of planar steel frames considering the effect of spread-ofplasticity, Structural Engineering & Mechanics, 11(4), 423–442, 2001. Leu, L. J., Yang, J. P., Tsai, M. H., and Yang, Y. B., Explicit inelastic stiffness for beam elements with uniform and nonuniform cross sections, Journal of Structural Engineering, ASCE, 134(4), 608–618, 2008. Li, T. Q., Choo, B. S., and Nethercot, D. A., Moment curvature relations for steel and composite beams, Steel Structures, Journal of Singapore Structural Steel Society, 4(1), 35–51, 1993. Liew, J. Y. R., White, D. W., and Chen, W. F., Beam-column design in steel frameworks-Insight on current methods and trends, Journal of Constructional Steel Research, 18, 259–308, 1991. Liew, J. Y. R., White, D. W., and Chen, W. F., Beam-columns, in constructional steel design, An international guide, Dowling P. J. et al., Eds., Elsevier, England, 105–132, 1992. Liew, J. Y. R., White, D. W., and Chen, W. F., Second-order refined plastic hinge analysis for framed design: Parts 1 and 2, Journal of Structural Engineering, ASCE, 119(11), 3196–3237, 1993a. Liew, J. Y. R., White, D. W., and Chen, W. F., Limit states design of semi-rigid frames using advanced analysis, Part 1: Connection modelling and classification; Part 2: Analysis and design, Journal of Constructional Steel Research, 26(1), 1–57, 1993b. Liew, J. Y. R., White, D. W., and Chen, W. F., Notional load plastic hinge method for frame design, Journal of Structural Engineering, ASCE , 120(5), 1434–1454, 1994. Liew, J. Y. R., Punniyakotty, N. M., and Shanmugam, N. E., Advanced analysis and design of spatial structures, Journal of Constructional Steel Research, 42(1), 21–48, 1997a.


247

Liew, J. Y. R., Yu, C. H., and Ng, Y. H., and Shanmugam, N. E., Testing of semi-rigid unbraced frames for calibration of second-order inelastic analysis, Journal of Constructional Steel Research, 41(2/3), 159–195, 1997b. Liew, J. Y. R, Tang, L. K., Holmaas, T., and Choo, Y. S., Advanced analysis for the assessment of steel frames in fire, Journal of Constructional Steel Research, 47(1–2), 19–45, 1998. Liew, J. Y. R., Chen, W. F., and Chen, H., Advanced inelastic analysis of frame structures, Journal of Constructional Steel Research, 55(1–3), 245–265, 2000a. Liew, J. Y. R., Chen, H., Shanmugam, N. E., and Chen, W. F., Improved nonlinear plastic hinge analysis of space frame structures, Engineering Structures, 22, 1324–1338, 2000b. Liew, J. Y. R., Teo, T. H., Shanmugam, N. E., Testing of steel-concrete composite connections and appraisal of results, Journal of Constructional Steel Research, 56, 117–150, 2000c. Liew, J. Y. R. and Tang, L. K., Advanced plastic hinge analysis for the design of tubular space frames, Engineering Structures, 22(7), 769–783, 2000. Liew, J. Y. R., A resource for structural steel design and construction, SSSS/BCA Joint Publication, Singapore, 83pp., 2001a. Liew, J. Y. R., State-of-the-art of advanced inelastic analysis of steel and composite structures, Steel and Composite Structures, 1(3), 341–354, 2001b. Liew, J. Y. R., Punniyakotty, N. M., and Shanmugam, N. E., Limit-state analysis and design of cable-tensioned structures, International Journal of Space Structures, 16(2), 95–110, 2001a. Liew, J. Y. R., Chen, H., and Shanmugam, N. E., Inelastic analysis of steel frames with composite beams, Journal of Structural Engineering, ASCE, 127(2), 361–370, 2001b. Liew, J. Y. R. and Uy, B., Advanced analysis of composite frames, Progress in Structural Engineering and Materials, 3, 159–169, 2001. Liew, J. Y. R., Buildable design of multi-storey and large-span steel structures, Steel Structures, 4, 53–70, 2004a. Liew, J. Y. R., Performance based fire safety design of structures—A multi-dimensional integration, Advances in Structural Engineering, 7(4), 111–133, 2004b. Liew, J. Y. R., Teo, T. H., and Shanmugam, N. E., Composite joints subject to reversal of loading, Part 1: Experimental study; Part 2: Analytical assessments, Journal of Constructional Steel Research, 60, 221– 268, 2004. Liew, J. Y. R. and Chen, H., Direct analysis for performance-based design of steel and composite structures, Progress in Structural Engineering and Materials, 6, 213–228, 2004a. Liew, J. Y. R. and Chen, H., Explosion and fire analysis of steel frames using fiber element approach, Journal of Structural Engineering, ASCE, 130(7), 991–1000, 2004b. Liew, J. Y. R. and Li, J. J., Advanced analysis of pre-tensioned bowstring structures, Steel Structures, 6, 153– 162, 2006. Liew, J. Y. R., Survivability of steel frame structures subject to blast and fire, Journal of Constructional Steel Research, 64(7–8), 854–866, 2008. Liew, J. Y. R. and Xiong, D. X., Effect of preload on axial capacity of concrete-filled composite columns, Journal of Constructional Steel Research, 65, 709–722, 2009. Lindner, J., Lateral torsional buckling of composite beams, Journal of Constructional Steel Research, 46(1–3), 222, 1998. Lorenz, B., Kato, B., and Chen, W. F. (eds.), Semi-rigid connections in steel frames, Council on Tall Buildings and Urban Habitat, Bethlehem, PA, 1993. Lui, E. M. and Ma, G., Analysis and design form stability in the U.S.—An overview, Steel and Composite Structures, 5(2–3), 103–126, 2005. Ma, K. Y. and Liew, J. Y. R., Nonlinear plastic hinge analysis of 3-D steel frames in fire, Journal of Structural Engineering, ASCE, 130(7), 981–990, 2004. Marshall, P., Lewis, D., and Stock, D., Yield interaction surface of an enhanced LeTourneau 116C chord, Marine Structures, 14, 379–396, 2001. Meek, J. L., and Loganathan, S., Large displacement analysis of space-frame structures, Computer Methods in Applied Mechanics and Engineering, 72, 57–75, 1989. Merchant, W., The failure load of rigid jointed frameworks as influenced by stability, The Structural Engineer, 32, 185–190, 1954.

248


Moan, T., Amdahl, J., Granli, T., and Hellan, Ø., Collapse behaviour of offshore structural systems, 2nd Int. Conf. on Advances in Marine Structures, Dunfermline, Scotland, 21–24 May, 1991. Murtha-Smith, E., Compression member models for space trusses: review, Journal of Structural Engineering, ASCE, 120(9), 2717–2147, 1994. Nethercot, D. A., Steel beam to column connections - A review of test data and their applicability to the evaluation of the joint behaviour of the performance of steel frames, CIRIA, London, 1985. Nethercot, D. A. and Zandonini, R., Methods of prediction of joint behaviour: beam-to-column connections, in Structural Connections, Stability and Strength, R. Narayanan, ed., Elsevier, London, 23–62, 1989. Nethercot, D. A., Li, T. Q., and Ahmed, B., Unified classification system for beam to column connections, Journal of Constructional Steel Research, 45(1), 39–65, 1998. Nigam, N. C., Yielding in framed structures under dynamic loads, Journal of the Engineering Mechanics Division, ASCE, EM5, 687–709, 1970. Nukala, P. K. V. V. and White, D. W., A mixed finite element for three-dimensional nonlinear analysis of steel frames, Computer Methods in Applied Mechanics and Engineering, 193, 2507–2545, 2004. Oehlers, D. J. and Sved, G., Flexural strength of composite beams with limited slip capacity shear connectors, Journal of Structural Engineering, ASCE, 121(6), 932–938, 1995. Oran, C., Tangent stiffness in space frames, Journal of the Structural Division, ASCE, 99, 987–1001, 1973. Orbison, J. G., Nonlinear static analysis of three-dimensional steel frames, Report No. 82–6, Department of Structural Engineering, Cornell University, Ithaca, NY., 1982. Orbison, J. G., McGuire, W., and Abel, J. F., Yield surface applications in nonlinear steel frame analysis, Computer Methods in Applied Mechanics and Engineering, 33, 557–573, 1982. Osterrieder, P. and Kretzschmar, J., First hinge analysis for lateral buckling design of open thin-walled steel members, Journal of Constructional Steel Research, 62, 35–43, 2006. Papqdrakakis, M. and Papadopoulos, V., Computationally efficient method for the limit elasto plastic analysis of space frames, Computational Mech, 16,132–141, 1995. Pi, Y. L. and Trahair, N. S., Nonlinear inelastic analysis of steel beam-column, I: Theory; II: Application, Journal of Structural Engineering, ASCE, 120(7), 2041–2085, 1994. Porter, F. L. and Powell, G. H., Static and dynamic analysis of inelastic frame structures, Report No. EERC 713, Earthquake Engineering Research Centre, University of California, Berkeley, CA, 1971. Powell, G. H. and Chen, P. F., 3D beam-column element with generalised plastic hinges, Journal of Structural Engineering, ASCE, 112(7), 627–641, 1986. Przemieniecki, J. S., Theory of matrix structural analysis. McGraw-Hill, New York, 1968. Punniyakotty, N. M., Nonlinear analysis and design of spatial truss and flexible structures, Thesis presented to National University of Singapore, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Singapore, 1998. Qian, X. D., Static strength of thick-walled CHS joints and global frame behaviour, Thesis presented to National University of Singapore, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Singapore, 2005. Richard, R. M. and Abbott, B. J., Versatile elastic-plastic stress-strain formula, Journal of the Engineering Mechanics Division, ASCE, 101(4), 511–515, 1975. Saw, H. S. and Liew, J. Y. R., Assessment of current methods for the design of composite columns in buildings, Journal of Constructional Steel Research, 53(2), 121–147, 2000. SCI/BCSA, Joints in steel construction: Composite connection, Connection Group Publication 213, Steel Construction Institute, UK, 1998. Shanmugam, N. E. and Lakshmi, B., State of the art report on steel-concrete composite columns, Journal of Constructional Steel Research, 57, 1041–1080, 2001. Sherbourne, A. N. and Bahaari, M. R., Finite element prediction of end-plate bolted connection behaviour. I: Parametric Study, Journal of Structural Engineering, ASCE, 123(2), 157–164, 1997. Skallerud, B. and Amdahl, J., Nonlinear analysis of offshore structures. Research Studies Press, 2002. SNAME, Guidelines for Site Specific Assessment of Mobile Jack-up Units, Technical & Research Bulletin 5–5A, 1994.


249

Sohal, I. S. and Chen, W. F., Local buckling and sectional behaviour of fabricated tubes, Journal of Structural Engineering, ASCE, 113(3), 1073–1090, 1988. Surovek, A. E., White, D. W., and Leon, R. T., Direct analysis for design evaluation of partially restrained steel framing system, Journal of Structural Engineering, ASCE, 131(9), 1376–1389, 2005. Surovek, A. E., Guidelines for the use of direct second-order inelastic analysis in steel frame design, Report of the Special Project Committee on Advanced Analysis Technical Committee on Compression and Flexural Members of the Structural Engineering Institute of ASCE, 2007. Swanson, J. A., Kokan, D. S., and Leon, R. T., Advanced finite element modeling of bolted T-stub connection components, Journal of Constructional Steel Research, 58(5–8), 1015–1031, 2000. Søreide, T. H., Amdahl, J., Eberg, E., Holmås, T., and Hellan, Ø., USFOS—A computer program for progressive collapse analysis of steel offshore structures, Theory Manual, Report STF71 F88038, 6th revision. SINTEF Structures and Concrete, Trondheim, 1994. Taby, J. and Moan, T., Collapse and residual strength of damaged tubular members, Behaviour of Offshore Structures, BOSS’85, Amsterdam, 1985. Taranath, B. S., Structural analysis and design of tall buildings. McGraw-Hill, Singapore, 1988. Taranath, B. S., Steel, concrete and composite design of tall buildings, McGraw-Hill, New York, USA, 1998. Taucer, F., Spacone, E., and Filippou, F. C., A fiber beam-column element for seismic response analysis of concrete structures, Report No. UCB/EERC-91/17, University of California, Berkeley, CA, 1991. Teh, L. H. and Clarke, M. J., The implications of linearisations, Approximations and computation algorithms in the second-order analysis of frames, Research Report No. R733, Department of Civil Engineering, University of Sydney, Australia, 1996. Teh, L. H. and Clarke, M. J., New definition of conservative internal moments in space frames, Journal of Engineering Mechanics, ASCE, 123(2), 97–106, 1997. Teh, L. H. and Clarke, M. J., Corotational and Lagrangian formulations for elastic three dimensional beam finite elements, Journal of Constructional Steel Research, 48, 123–144, 1998. Teh, L. H. and Clarke, M. J., Symmetry of tangent stiffness matrices of 3D elastic frame, Journal of Structural Engineering, ASCE, 125(2), 248–251, 1999a. Teh, L. H. and Clarke, M. J., Plastic zone analysis of 3D steel frames using beam elements, Journal of Structural Engineering, ASCE, 125(11), 1328–1337, 1999b. Teh, L. H., Cubic beam elements in practical analysis and design of steel frames, Engineering Structures, 23, 1243–1255, 2001. Teh, L. H., Hsiao, K. M., White, D. W., and Ziemian, R. D., Exact tangent stiffness for imperfect beamcolumn members, Journal of Structural Engineering, ASCE, 127(12), 1490–1492, 2001. Timoshenko, S. P. and Gere, J. M., Theory of elastic stability, 2nd ed., McGraw-Hill, New York, 1961. Toma, S., Chen, W. F., and White, D. W., A selection of calibration frames in North America for second-order inelastic analysis, Engineering Structures, 17(2), 104–112, 1995. Trahair, N. S. and Chan, S. L., Out-of-plane advanced analysis of steel structures, Engineering Structures, 25, 1627–1637, 2003. Tschemmernegg, F. and Huber, G., Joint transformation, COST C1/WD2-96-09, 1996. Ueda, Y., Rashed, S. M. H., and Nakacho, K., New efficient and accurate method of nonlinear analysis of offshore tubular frames (the idealized structural unit method), Journal of Energy Resources Technology, 107, 204–201, 1985. Ueda, Y. and Rashed, S. M. H., Modern method of ultimate strength analysis of offshore structures, International Journal of Offshore and Polar Engineering, 1(1), 27–41, 1991. ULTIGUIDE, Best practice guidelines for use of non-linear analysis methods in documentation of ultimate limit states for jacket type offshore structures, Prepared by DNV-SINTEF-BOMEL, 1999. Uy, B. and Liew, J. Y. R., Chapter 51: Composite steel-concrete structures, In civil engineering handbook: 2nd Edition, Edited by Chen, W. F. and Liew, J. Y. R., CRC Press, Boca Raton, Florida, 2002. Uy, B., Strength of short concrete filled steel box columns incorporating local buckling, Journal of Structural Engineering, ASCE, 126(3), 341–352, 2000. Uy, B., Local and post-local buckling of fabricated steel and composite cross sections, Journal of Structural Engineering, ASCE, 127(6), 666–677, 2001.

250


van der Vegte, G. J. and Makino, Y., Numerical simulations of bolted connections: the implicit versus the explicit approach, Proceedings of Connections in Steel Structures V: Behaviour, Strength and Design, Amsterdam, Netherlands, June 3–4, 2004. Ultimate Strength, Proceedings of 16th International Ship and Offshore Structures Congress, 20-25 Aug 2006, Southampton, UK, 2006. USFOS, Ultimate Strength for Framed Offshore Structures, http://www.usfos.com, 2009. Van Long, H., Hung, N. D., Local buckling check according to Eurocode-3 for plastic-hinge analysis of 3-D steel frames, Engineering Structures, 30, 3105–3113, 2008. Viest, I. M., Colaco, J. P., Furlong, R. W., Griffis, L. G., Leon, R. T., and Wyllie, L. A., Composite construction design for buildings, McGraw Hill, New York, 1997. Vlasov, V. Z., Thin-walled elastic beams, 2nd ed. Moscow, USSR; English translation, Israel Program for Scientific Translation, Jerusalem, Israel, 1961. Vrcelj, Z., Bradford, M. A., and Uy, B., Elastic distortional buckling modes in continuous composite beams, Proceedings of the 16th Australasian Conference on the Mechanics of Structures and Materials, Sydney, Balkema, 327–333, 1999. Vrcelj, Z. and Uy, B., Strength of slender concrete-filled steel box columns incorporating local buckling, Journal of Constructional Steel Research, 58(2), 275–300, 2002. White, D. W., Material and geometric nonlinear analysis of local planar behavior in steel frames using interactive computer graphics, Report No. 86–4, Department of Structural Engineering, Cornell University, Ithaca, NY., 1986. White, D. W. and Chen, W. F., Introduction, in plastic hinge based methods for advanced analysis and design of steel frames—An assessment of the state-of-the-art, Structural Stability Research Council, Lehigh University, Bethlehem, PA., 1–22, 1993. White, D. W. Comprehensive performance assessment of building structural systems: research to practice, Engineering Structures, 18(10), 778–785, 1996. White, D. W., Surovek, A. E., Alemdar, B. N., Chang, C-J., Kim, Y. D., and Kuchenbecker, G. H., Stability analysis and design of steel building frames using the 2005 AISC Specification, Steel Structures, 6, 71–91, 2006. Wong, M. B. and Tin-Loi, F., Yield surface linearization in elastoplastic analysis, Computers and Structures, 26(6), 951–956, 1987. Wongkaew, K. and Chen, W. F., Consideration of out-of-plane buckling in advanced analysis for planar steel frame design, Journal of Constructional Steel Research, 58, 943–965, 2002. Yang, Y. B. and McGuire, W., Stiffness matrix for geometric nonlinear analysis, Journal of Structural Engineering, ASCE, 112(4), 853–877, 1986a. Yang, Y. B. and McGuire, W., Joint rotation and geometric nonlinear analysis, Journal of Structural Engineering, ASCE, 112(4), 879–905, 1986b. Yang, Y. B. and Fan, H. T., Yield surface modelling of I-sections with non-uniform torsion, Journal of Structural Engineering, ASCE, 114(6), 953–972, 1988. Yang, Y. B., Chern, S. M., and Fan, H. T., Yield surface for I-sections with bimoments, Journal of Structural Engineering, ASCE, 115(12), 3044–3058, 1989. Yang, Y. B., Kuo, S. R., Theory and analysis of nonlinear framed structures, Prentice Hall, Singapore, 1994. Yang, Y. B., Leu, L. L., Nonlinear stiffnesses in analysis of planar frames, Computer Methods in Applied Mechanics and Engineering, 117, 233–247, 1994. Yang, Y. B., Kuo, S. R., Wu, Y. S., Incrementally small-deformation theory for nonlinear analysis of structural frames, Engineering Structures, 24, 783–798, 2002. Yura, J., Zettlemoyer, N., and Edwards, I. F., Ultimate capacity equation for circular tubular joints, Proc of Offshore Technology Conference, Paper OTC 3690, Texas, 113–126, 1980. Zayas, V. A., Mahin, S. A., and Popov, E. P., Cyclic inelastic behavior of steel offshore structures, University of California. UCB/EERC-80/27. Aug., 1980. Ziemian, R. D., Advanced methods of inelastic analysis in the limit states design of steel structures, Thesis presented to Cornell University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy, Ithaca, NY., 1990.


251

Ziemian, R. D., McGuire, W., Deierlein, G. G., Inelastic limit states design. Part I: Planar frames studies. Part II. Three-dimensional frame design, Journal of Structural Engineering, ASCE, 118(9), 2532–2567, 1992. Ziemian, R. D., McGuire, W., Modified tangent modulus approach, a contribution to plastic hinge analysis, Journal of Structural Engineering, ASCE, 128(10), 1301–1307, 2002.

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Appendix 1 Elastic Stiffness Matrix, ke

 k e1 k e 2  ke 3 ke =    Sym. 

− k e1 − keT2 k e1

ke 2 k e4 − ke 2 ke 3

     

(A1.1)

in which:

 EA / L 0 0  0 12 EI z′ / L3 0 k e1 =  0 0 12 EI y′ / L3 

 0 0  0 0 k e2 =  2  0 −6 EI y′ / L

 GJ / L  0 k e3 =   0 

 −GJ / L  0 k e4 =   0 

(

0 6 EI z′ / L2 0

0 4 + ηy EI y′ / L 0

)

   

(A1.2)

   

(A1.3) 0 0

(4 + η ) z

0

( 2 − η ) EI ′ / L y

0

y

   EI z′ / L   0 0

(2 − η ) z

   EI z′ / L  

(A1.4)

(A1.5)

12 EI y EI n 12 EI z , ηy = , ηz = , and An is the shear area along axis n. If the 2 1 + φn GAz L GAy L2 effect of shear deformation is ignored, ηy = ηz = 0. L is the element length at C1 based on the UL formulation. where EI n′ =


253

Appendix 2 Geometric Stiffness Matrix, kg

 k g1 k g 2  kg 4 k g =    Sym.

where:

 0  k g1 =   Sym. 

(M

k g2

 0  M /L ya =  M za / L 

k g3

 0  M /L yb =  M zb / L 

k g4

k g5

  =     =  

− k g1 kg5 k g1

kg3 kg6 − kg3 kg 4

)

+ M zb / L2

za

φ1z + Fxb / L 0

−φ 2 y 0

0 φ 2 z − M xb / L

− M xb / L −φ 2 y

    

)

(

 −K / L − M za + M zb / 6  −φ 4 y =  − M za + M zb / 6   M +M /6 − M xb / 2 ya yb 

(

)

φ1n = 2 EI n ( S1n + S2 n − 6 ) / L3

(

)

za

(

)

φ2 n = EI n ( S1n + S2 n − 6 ) / L2 φ3n = EI n ( S1n − 4 ) / L

φ4 n = EI n ( 2 − S2 n ) / L

(A2.2)

(A2.3)

(A2.4)

)

+ M zb / 6 − M ya + M yb / 6    0 φ3 y  φ3 z Sym.  0 − M ya / L − M za / L   φ2 y  0 − M xb / L −φ 2 z − M xb / L  0  K/L

k g6

)

(

− M ya + M yb / L2   0   φ1 y + Fxb / L 

   M xb / L  

(A2.1)

0 φ2 z

M xb / L

(M

     

(M

(A2.5)

(A2.6)

)

+ M yb / 6    M xb / 2   −φ 4 z 

ya

(A2.7)

(A2.8)

(A2.9)

(A2.10)

(A2.11)

In the above matrices, the underlined coupling terms are lost in geometric stiffness matrix, kʹg, based on the beam-column approach. L is the element length at C1 based on the UL formulation.

Appendix 3 Bowing Matrix, kb k b = k b1 + T T k b2 T

(A3.1)

in which:  EI EA EI k b1 = Diag  3 − , 0, 0, 0, 0, 0, 3 − HL0  HL0 L0  G2 G G G1z G1 y G1z G2 y 1z 1z 2 z  2 G2 z G2 z G1 y G2 z G2 y  EI  G12y G1 y G2 y k b2 =  HL0  G22y    Sym.    T=    

0 1/ L 0 1/ L 0 0 0 0 0 0 −1 0

0 0 −1 / L −1 / L 0 0

I = I y + Iz

0 0 0 0 −1 0

0 0 1 0 0 0

1 0 0 0 0 0

 EA , 0, 0, 0, 0, 0  L0  0 G1z / L0   0 G2 z / L0   0 G1 y / L0  0 G2 y / L0   0 0  0 

0 −1 / L 0 0 −1 / L 0 1/ L 0 0 0 0 1/ L 0 0 0 1 0 0

0 0 0 0 1 0

0 0 0 1 0 0

0 1 0 0 0 0

(A3.2)

(A3.3)

       

(A3.4)

(A3.5)

G1n = S1′n Θ na + S2′n Θ nb + c0′ n (δ n / L0

(A3.6)

0

(A3.7)

(A3.8)

(A3.9)

(A3.10)

G2 n = S2′n Θ na + S1′n Θ nb − c0′ n S1′n = 2 ( b1n + b2 n S21′ n = 2 ( b1n − b2 n

) (δ / L ) n

) )

c0′ n = bvsn H=

1 I − ∑  b1′n ( Θ na + Θ nb 2 I AL0 n = z , y n 

)

2

+ b2′n ( Θ na − Θ nb

)

2

)

)

)

2 + bvsn ′ (δ n / L ( Θ na − Θ nb + bvvn ′ (δ n / L0  

(A3.11)

In the above equations a prime superscript denotes the differentiation with respect to qn, L0 is the initial member length, L is the element length at C1 based on the UL formulation.

7

Case Studies for Second-order (Direct) Analysis of Semi-rigid Frames in Hong Kong

Y. P. Liu Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong. Dennis Lam Department of Civil Engineering, University of Leeds, U.K. S. L. Chan Department of Civil and Structural Engineering, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.

7.1 Introduction........................................................................................................................... 000 7.2 Second-order Integrated Design and Analysis.................................................................. 000 P-Δ and P-δ effects • Initial Imperfections 7.3 Modeling of Semi-rigid Jointed Members......................................................................... 000 7.4 Examples................................................................................................................................. 000 Example 1: The Hemispherical Dome at Roof of a Building • Example 2: The Shallow Roof at the Top of a Building

7.1 Introduction After decades of research by Liew et al. (1993), Zhou and Chan (1995), White and Hajjar (2000), Hetao and Li (2009), and others, the technology of the simulation-based design of steel structures has been matured and is practically feasible with recommendations given in various codes such as The Code of Practice for Structural Uses of Steel Hong Kong (COPHK, 2005) and the Eurocode 3 (CEN, 2005). While the theoretical background, previous works, and research in the topic of semi-rigid frames have been described in detail in previous chapters, the report of second-order analysis of semi-rigid frames is rather limited in literature because of several issues. First, the stiffness, ductility, and strength of the connections are not comprehensive and engineers are not fully aware of the tested data in the appendix of this book. Second, code requires engineers to

255

256


consider either strength for rigid connections or ductility for rotational ductility for pinned connections. However, for elastic-plastic or advanced analysis of semi-rigid frames, both these effects are required in checking the adequacy of connections. Finally, the computational technique for semi-rigid connections is not yet well known to engineers. It has been well recognized that semi-rigid connection not only provides a more accurate picture on the actual response of a structure, it also provides a more economical solution to a design because the moments at midspan and ends of a beam are more balanced. This chapter details some of the previous work by the authors on the design of bare steel frames in Hong Kong and Macau using the concept and the method. One hemispherical dome constructed in Hong Kong and one shallow roof built in Macau are studied in Examples 1 and 2, respectively. Both are predominantly under strong wind and the use of the elastic critical load factor for frame classification is rather irrelevant. The buckling length of the member is difficult to estimate as the ends of the member are displaced. When using the proposed second-order or direct analysis in LRFD terminology, the member resistance can be computed directly by a simulation process, and the sectional strength is directly checked.

7.2 Second-order Integrated Design and Analysis The conventional linear design method divides the whole design procedure into two stages: (1) determination of the internal forces and moments acting on each member of the structural system by elastic linear analysis, and (2) assessment of the strength and stability of each member treated as an isolated member by plastic analysis. Compatibility between the isolated member and the structural system is doubtable. There is an increase in awareness for the use of secondorder analysis that simulates directly the behavior of structural members, connections, and other components in the determination of overall system response. The new and advanced nonlinear integrated design and analysis method is significantly different from the conventional linear design since the nonlinear analysis model contains more factors, which may significantly affect the structure behaviors. Also, the interaction between the structural members and the structural system can be considered. Generally speaking, the nonlinear design method is a system-based approach in contrast to the traditional member-based design method. The special features of the second-order analysis are that the P-Δ and P-δ effects as well as the initial imperfections should be considered in the analysis stage.

7.2.1 P-Δ and P-δ Effects

When a structure deforms grossly, the original geometry can no longer be employed for the formulation of the transformation matrix simply because the coordinates have been changed. This effect, named the P-Δ effect, may become important when the deflection or the conjugate force is large, such as the case of a building under a heavy mass at the roof and a lateral wind load. An additional moment as the P-Δ moment will be induced due to this effect. The P-δ effect is referred to as the second-order effect due to the deflection along a member and the axial force. It affects the state of stress as well as the stiffness of the member. Like the P-Δ effect, an additional moment named P-δ moment will be induced due to the P-δ effect. Its careful consideration is important for buckling analysis and design of slender skeletal structures. In general, both the P-Δ (frame sidesway) and P-δ effects (member curvature) will occur in a structure under vertical and horizontal external forces. These effects are shown in Figure 7.1.


In this chapter, the P-Δ effect is automatically considered in the nonlinear incremental-iterative procedure while the P-δ effect is accounted for by the use of the Pointwise Equilibrium Polynomial (PEP) element (Chan and Zhou, 1995) at the element level.

257

P

P

∆

7.2.2 Initial Imperfections

As there are no perfect structures or structures that are free from defects due to initial crookedness and residual stress, imperfections must be considered when using the second-order analysis and advanced analysis (COPHK, 2005) for practical design. Two types of imperfections should be included in the nonlinear analysis and design (i.e., the member and frame imperfections).

δ

7.2.2.1 Member Imperfections

Member initial imperfections are due to either initial geometric FIGURE 7.1 The P-Δ and imperfections or residual stresses or both. The initial geometric P-δ effects. imperfections of members may be due to one or several aspects such as cambering, sweeping, twist, out-of-straightness and cross-section distortion. The residual stresses in members may be due to manufacturing and fabrication processes, erection out-of-fit, and construction sequencing. To account rigorously and exactly for all the imperfections seems impossible. Practically, they can be simulated in the analysis or design model by the equivalent initial bow imperfection, which may be slightly different in the national design codes due to the difference in steel products. According to COPHK (2005), the equivalent initial bow imperfections for different sections are specified in Table 6.1. These values may be used in a second-order analysis for the steel members under compression. For composite column, the buckling curves and member imperfections are specified in Table 10.13 of COPHK (2005).

7.2.2.2 Frame Imperfections

The frame imperfections are mainly due to the out of plumbness of frame and column in the erection processes and construction sequence. This type of imperfection may increase the sway effect and induce P-Δ moments, especially when the structure is subjected to large vertical loads. First-order linear analysis uses the moment amplification to enlarge the linear moment for sway effect, which can be due to wind load or notional force normally taken as 0.5 percent for permanent structures and 1 percent for temporary structures. In second-order analysis, wind load or notional force are still used, but an alternative, more reliable, and convenient method is to use the elastic buckling mode as the imperfection mode with amplitude set equal to the out-of-plumbness normally taken as 1/200 of building height according to COPHK (2005) or other justified values.

7.3 Modeling of Semi-rigid Jointed Members A semi-rigid connection must have the required strength, stiffness, and ductility. Some typical moment versus rotation (M-θr) curves and various analytical and mathematical models representing the M-θr relationships can be found in previous chapters. Conveniently, a joint can be considered in an analysis as dimensionless with the location at the intersection of the element

258


center lines. Further, a rotational spring element satisfying the M-θr relationship is inserted into each end-of-beam element to model the connection behavior. The joint equilibrium condition can be expressed as: i =0 Me + M

(7.1)

in which Me and Mi are the moments at the two ends of a connection (see Figure 7.2a). The corresponding external node is connected to the global node, and the internal node is joined to the beam element. The stiffness of the connection S can be related to relative rotations at the two ends of the connection spring as: S=

Me Mi = (θe − θi ) (θi − θe )

(7.2)

where θe and θi are the conjugate rotations for the moments Me and Mi (see Figure 7.2b). Rewriting Equation 7.2 in matrix form, the stiffness matrix of a connection spring can be written as: − S   θe  =  M e      S   θi   M i  A typical beam element bending stiffness matrix can be expressed as:  S  − S

(7.3)

 k11 k12   θ1i   M1i  (7.4)     =   k 21 k22   θ 2 i   M 2i  in which kij is the stiffness coefficient of a prismatic beam. Here, the imperfect PEP element proposed by Chan and Zhou (1995) is adopted and more details can be referred to the original reference. Therefore, a hybrid element can be obtained by directly adding the connection stiffness of the two ends to the PEP element bending stiffness matrix as:

 S1   − S1  0  0 

− S1 k11 + S1 k 21 0

0 0 k12 0 k 22 + S2 − S2 S2 − S2

     

θ1e θ1i θ 2i θ 2e

    =      

M1e M1i M 2i M 2e

     

(7.5)

in which the first subscript refers to node 1 or node 2. The internal degrees of freedom of the stiffness expression can be eliminated by a standard static condensation procedure. The stiff-

y

Me Global Node

Mi

Beam

(a) Equilibrium at a joint

θ2e

θ1i θ1e

Node 1

θ2i

Node 2

(b) The external and internal rotations

FIGURE 7.2 Modeling of semi-rigid jointed member.

x


259

ness expression of a beam element with both ends connected to a pair of springs can be finally written as:  ke  θe  =  M e 

in which:

(7.6)

T

θe  =  θ1e θ 2 e  ,  M e  =  M1e   

M 2e  

T

 k12 S1 S2 1  S β − S12 ( S2 + k 22 )  ke  =  1  2 β  k 21 S1 S2 S2 β − S2 ( S1 + k11 ) 

(7.7) (7.8)

and β is given by:

β = det

k11 + S1 k 21

k12 k 22 + S2

(7.9)

where S1 and S2 are the connection stiffness at nodes 1 and 2, respectively. When the spring stiffness Si is zero, it means that the corresponding end is pinned end; when the spring stiffness Si is infinite, it means that the corresponding end is the rigid end. For the semi-rigid case, the spring stiffness Si can be determined by the given M-θr function.

7.4 Examples 7.4.1 Example 1: The Hemispherical Dome on the Roof of a Building

The design of a single-layered semispherical dome shaped steel roof of a building is described here. This type of dome structure is a common architectural feature, and is usually slender, because of aesthetic requirement, and under low loads. However, they can be under high wind load as they are widely constructed in open areas and at the roof of high-rise buildings. This structural form always poses a challenge to the structural engineer for special requirement as most of them cannot be classified as standard or typical structures such that the use of many formulae in codes are inapplicable. For example, the method of frame classification for rectilinear frames cannot be used here as buckling is due to horizontal wind loads causing tension in members on one side and compression in members on the other side, which is in contrast to typical building frames under gravitational dead and live loads. On the other hand, this type of dome structure is quite common to-date for construction as aesthetic and monumental building construction. The computer image of the dome is shown in Figure 7.3.

7.4.1.1 Structure Description

The dome frame is located at the roof top and a multistory building with a height of 178.25 m above mean sea level, where as the top roof of a services apartment

FIGURE 7.3 The single-layered semispherical dome at the roof of a building.

260


and the members of the dome are circular hollow sections with a single bolt at the ends and connected to steel balls. The diameter of the dome is 18.95 m above concrete plinth level and the main member of the dome is 139.7 × 5 mm circular hollow sections of grade S235 steel. Two inner frames are constructed with location at the top and the bottom levels of the dome in order to enhance the rigidity of the frame, and these inner frames are made of 48.3 × 3.2 mmthick CHS sections of Grade S235. The dome is further supported by a ring beam of 254 × 254 × 132 UC of Grade S275 steel with 8 nos. of 457 × 16 mm-thick CHS sections of Grade S355 below the ring beam as the steel column supporting the dome frame. The 8 nos. of steel column are supported by the existing reinforced concrete (RC) beams. In addition, a 7 m-long steel pole is fixed at the top of the dome. The main members of the dome are connected by a bolted ball joint, and the ball joint, with multiconnection holes, is adopted as semi-rigid connection of the main members. However, the ball joint at the bottom layer of the dome is connected to the ring beam by the bolt and assumed as a pinned connection. The circular steel column is connected to the ring beam by welding and the other end of the column is connected to the RC plinth by cast-in grade 8.8 steel bolts. In structural analysis, the steel columns are assumed to be pinned at the base and supported on the existing RC beam. The pinned assumption for the dome leads to a mechanism, and therefore a larger size bolt of diameter, an M27 bolt, is used and assumed as a semi-rigid joint providing stability to the complete frame. The stiffness of this connection made of an M27 bolt is taken as 4EI/L in which E is the Young’s modulus of elasticity for steel, I is the second moment of area of the bolt, and L is the extruded bolt length.

7.4.1.2 Load Path

Wind load and live load act along the members together with their self-weight. The applied loads from the main members will be transferred to the ring beam of the dome. The loading of the ring beam will then be passed to the steel columns and then to the existing RC elements. It is assumed the connections between main members of the dome are pinned, rigid, and semi-rigid connections. All base connections to concrete plinth are assumed pinned in order to transfer minimum moment to the supporting concrete structure.

7.4.1.3 Computer Method of Analysis

The three-dimensional analysis model is used in determining the forces in members and in connections. The structure is analyzed by second-order first-plastic hinge (P-Δ-δ) analysis. The first-order linear analysis requires assumption of effective length, which cannot be determined accurately and scientifically in the present structural form. Further, the snap-through type of buckling for modules under wind involves significant deformation, which violates the underlying assumption for the effective length method as the frame does not deform until elastic eigen-buckling occurs. Once the force is applied onto the frame, its members deflect and the second-order stress magnifies. The structure is imperfection sensitive and therefore the eigen-buckling load carries little physical significance here. In the second-order analysis used by the authors, both the imperfections at local member and global frame levels are considered with values adopted directly from the code respectively as span/500 and height/200. These numbers are input into the software NIDA (2008), which automatically considers the effects by assuming appropriate member curvature and imperfect frame geometry before load is applied to the frame (Chan and Zhou, 2004). For checking of structural stability and adequacy, the design load under combined and factored load cases is used and applied to the frame in the analysis. The cross-sectional strength check in Equation 1 below is then applied to monitor the structural adequacy at every section along all members. For the first-plastic-hinge analysis, any sectional strength failure indicates the inadequacy of the frame,


261

Divergence Load

Load, F

KT

∆F0

Equilibrium Path

∆F1

∆u0

∆u1

Displacement, u FIGURE 7.4 The constant load Newton-Raphson method.

and the member size or steel grade must be increased. Figure 7.4 shows the process of checking for stability and strength by the Newton-Raphson method. Note that this approach is adopted to deal with many combined load cases with each combined load case considered in a single and separate analysis. The method is used as a standard design procedure for any member checked under the ultimate-limit state.

)

(

)

M y + Fc ∆ y + δ y M + Fc ( ∆ x + δ x Fc + x + = φ ≤1 Ag Py M cx M cy

(7.10)

in which Fc is the axial force, Ag is the cross-sectional area, py is the design strength, Mcx and Mcy are the moment capacities about the principal x- and y-axes, Mx and My are the bending moment about the principal axes, Δ and δ are the global frame and local member second-order deflection, and ϕ is the section capacity factor. When the advanced analysis allowing for plastic hinges is used for determination of the ultimate resistance of the structure, the yielded section is assumed to possess a plastic hinge when zero tangential stiffness (taken as 0.1 percent of the elastic stiffness in computer to avoid numerical overflow), and plastic moment—reduced for presence of axial force—is assumed in the section that can carry no further load with limiting capacity equal to the instance of force and moment in Equation 7.10. Owing to the change of geometric and material properties during a load increment, the applied force will not be absolutely balanced by the resistance. The iterations are needed to dissipate the unbalanced forces between the applied (action) and resistance forces. This unbalanced force is then used as a new set of external loads applied to the structure with the process repeated until the norm of the unbalanced forces is sufficiently small or less than 0.1 percent in our studies. The process is repeated and incremented until the collapse load is reached with the collapse load factor determined. The procedure is adopted for progressive collapse analysis of finding the true collapse load and the identification of key elements, which are defined as members with their failure causing more than a certain area of collapse. In some codes, the area is taken as 70 m2.

7.4.1.4 Design Code

7.4.1.4.1 Material Properties There are three types of structural steel, which should be conformed to the requirements of COPHK (2005) and are used for the steel members as shown in Table 7.1.

262


TABLE 7.1 Material properties of steel Material

Elastic modulus (kN/m2)

Poisson’s Ratio

Design strength py (kN/m2)

Unit weight (kN/m3)

S235

2.05 × 108

0.3

2.35 × 105

77

S275

2.05 × 108

0.3

2.75 × 105

77

S355

2.05 × 10

0.3

3.55 × 10

77

8

5

Note: 1. All welds must be compatible or over-matching to steel grade used 2. Design strength py for Hot Rolled section and other welded plates

Steel grade S235 S275 S355

Thickness less than or equal to (mm)

Design strength py (N/mm2)

16

235

40

225

16

275

40

265

16

355

40

345

3. For welded section under compression, py should be reduced by 20 N/mm2 for reduction due to welding residual stress

7.4.1.4.2 Section Assignment and Connections The size of members is CHS 139.7 × 5 for those in the dome, CHS219.1 × 8 for the pole, CHS48.3 × 3.2 for beams, and UC254 × 254 × 132 for columns. For the steel bolts, the ISO grade 8.8 bolts are used and the weld grade of E42, in compliance with the code requirements, is adopted. 7.4.1.4.3 Load Combination The basic load cases include dead loads, live loads, wind loads, and temperature loads. The average temperature in Hong Kong is coded from +0.1°C to +40.0°C. The basic design wind pressure is 3.2 kPa for the height 178.25 m above mean sea level according to the HKWC (2004). A shape pressure coefficient Cp of 2.0 for individual members of an open framework building is multiplied to the basic design wind pressure. According to COPHK (2005), the following partial load factors and combinations for normal ultimate-limit state shall be applied to strength and stability for normal design situations. Table 7.2 is a summarization of the partial load factors and combination.

7.4.1.5 Boundary Conditions

The 8 nos. of steel columns made of 457 × 16 mm-thick CHS sections of Grade S355 are pinned to the RC beams and columns because the concrete cannot resist the large moments from the base of stanchions.


A sensitivity study for elastic critical load factor λcr against the rigidity of the ball joint of the dome is carried out to investigate the effects of rotational stiffness of the joint. The computed results are summarized in Table 7.3.


263

TABLE 7.2 Partial load factors according to COPHK (2005) Partial load factors for load type

Load combination

Dead Gk

Imposed Qk

Wind Wk Temperature Tk

Adverse Beneficial Adverse Beneficial 1. Dead and imposed

1.4

1.0

1.6

0

—

1.2

2. Dead and lateral

1.4

1.0

—

—

1.4

—

3. Dead, lateral and imposed

1.2

1.0

1.2

0

1.2

1.2

TABLE 7.3 Numerical results λcr

Maximum end moment of the dome member (kNm)

All rigid

39.2

17.8

All pinned

0.08

0

Only bottom layer pinned and others are rigid

32

4.0

Semi-rigid with rotational stiffness = 135kNm/ rad (M27 bolt)

7.8

1.3

Semi-rigid with rotational stiffness = 5kNm/rad (M12 bolt)

0.6

0.05

Semi-rigid with rotational stiffness = 1600kNm/ rad (Hexagonal nut of diameter 50mm)

35.7

8.23

Connection type

For semi-rigid connections with M27 bolts, the stiffness of semi-rigid connection is taken as 135 kNm/rad as the rotational stiffness of the joints. This value of joint stiffness is calculated from the length of cross-sectional diameter of the connecting bolt as 4EI/L of the bolt in which E is the Young’s modulus of elasticity of steel, I is the second moment of area, and L is the length of the bolt. For rigid and pinned connections, respectively infinite and zero joint stiffness is assumed for the connection stiffness of every member. The rotational stiffnesses are evaluated by 4EI/L where L = 160mm. The assumed length of bolt L is longer than the actual extruded length of the bolt in order to allow for fitting tolerance, which makes the connection more flexible. All critical members are found in the bottom level of the dome under the combined load case of wind and dead loads.

7.4.1.7 Imperfections

There are no perfect structures or structures that are free from defects, due to initial crookedness and residual stress; imperfections must therefore be considered when using the second-order analysis and advanced analysis to COPHK (2005). Below is a description of codified consideration for member and for frame imperfections. 7.4.1.7.1 Member Imperfections For hot-rolled hollow sections, Curve A in Table 6.1 in COPHK (2005) is used. Thus, member imperfection equal to span/500 is assumed. For other types of profiled steel section, a larger

264


imperfection may be used and the values of these member types can be found by curve-fitting of buckling experimental curves or design curves from any codes. 7.4.1.7.2 Frame Imperfections The out-of-plumbness equal to the height/200 to COPHK (2005) is assumed. For domes, the frame imperfection can also be taken as span/200 in accordance with the Chinese Technical Specification for latticed shells (JGJ61-2003).

7.4.1.8 Additional Vibration Frequency

According to clause 7.6 of the Code of Practice on Wind Effects in Hong Kong 2004 (HKWC, 2004), the natural frequency should be greater than 0.2 Hz for no resonance with wind action. The period of the whole dome frame is found to be 0.62 of a second (i.e., 1.61 Hz), and therefore it is acceptable.

7.4.1.9 Load Carrying Capacity

As mentioned before, three conditions for connection stiffness are assumed and their design adequacy is investigated. Only the case of semi-rigid connecting stiffness with a stiffness value equal to 135 kNm/radian is satisfactory for the design. Therefore, the M27 bolts are used. Further fullscale tests for connections are conducted to confirm the achievement of this value in the connection type. It is of interest to note that the pinned assumption for connections is unable to provide a valid solution to the design because of low stiffness. On the other hand, the rigid assumption cannot be achievable in experimental tests. Further, because of the presence of large moment at member ends, the section capacity check cannot be passed for connecting members or the bolts. Therefore, the present approach represents a realistic assumption for the dome design. Also, no assumption for the effective length has been made for the complete design process.

7.4.2 Example 2: The Shallow Roof at the Top of a Building 7.4.2.1 Structure Description

The shallow roof steel frame, which is arch dome shaped with a 57.04 m span, 62.24 length, and 11.81 m height is located at the roof top of a three-story building. This steel roof is the supporting structure for the glass skylight and curtain walls at two ends (see Figures 7.5 and 7.6). The arch main beams are of 660 mm height and designed for resisting the vertical loads such as dead loads, service loads, and wind loads. At the four edges of the roof, bracings are used to provide lateral stiffness and to resist the horizontal wind loads. The vertical loads are first transferred to the secondary purlins and then to the arch main beams. The lateral restraint due to glass panels is weak and is normally ignored. Therefore, the purlins are made of an RHS section so that the lateral-torsional buckling can be avoided. It is noted that the roof structure cannot perfectly locate on the RC columns as the tensile strength of concrete is small. Thus, two continuous steel beams made of a box section of 650 mm height are used to support the arch main beams. The box section has a relatively large torsional constant and therefore the two continuous beams will not fail in torsional moments or by lateraltorsional buckling. The curtain walls at two ends are of 11.81m height and subjected to large wind loads. It is easy to pass the ultimate-limit state checking, but the checking for serviceability limit state requires deep vertical beams to reduce the deflection. Therefore, the members in curtain walls are made of Chinese steel of Grade Q235 for economical design. For architectural reasons, the arch main beams are continuous and the splice joints are made of full-strength butt weld. In such a case, the fully rigid connections for the arch main beams are


265

FIGURE 7.5 The single-layered shallow roof of a building (as built).

Arch main beams

Secondary purlins

FIGURE 7.6 The singlelayered shallow roof of a building (computer model).

reasonably in line with the current engineering practice. Also, welded connections rather than bolted connections are adopted for the connections between the secondary purlins to the arch main beams. For economical design, the welded connection is made of fillet weld, and therefore ultrasonic examination is avoided. However, the modeling of this type of welded connection in an analysis is debatable. Basically, two types of assumptions of this connection are widely made in practice (i.e., the fully rigid connection and the ideally pinned connection). This example aims to discuss the influence of the different modeling of this type of connection.

7.4.2.2 Load Path

For the skylight, the pressures due to the weight of glass panels and pipework, live loads, and wind loads are applied to the secondary purlins of rectangular hollow sections of galvanized mild steel,

266


and then transferred to the arch main beams of the built-up galvanized H mild steel section. The service loads are added directly to the arch main beam as point loads. For the curtain walls, the pressures due to the weight of glass panels and due to wind are applied to the secondary purlins and then transferred to the main arch beams, made of built-up galvanized mild steel H section. The arch system is supported on the steel beams of box section and further pinned to the concrete structure. The two curtain walls are supported on concrete beams with the pinned assumption.

7.4.2.3 Computer Method of Analysis

The three-dimensional analysis model is used in determining the forces in members and in connections. The structure is analyzed by second-order elastic (P-Δ-δ) analysis. The same theory and procedure used in Example 1 are used in this example.

7.4.2.4 Design Code

7.4.2.4.1 Material Properties Two types of structural steel conformed to the requirements of COPHK (2005) are used for the steel members as shown in Table 7.4. 7.4.2.4.2 Section Assignment and Connections The size of the members are 660 × 350 × 20 × 12 I-section for the main beams, RHS250 × 150 × 5 for the secondary purlins, built-up box section 650 × 550 × 20 for two supporting beams, and 560 × 300 × 16 × 12 I-section for bracing members. The members in curtain walls are mainly made of RHS sections. Fillet weld is adopted for the connections between arch main beams and the secondary purlins. All other member-to-member connections of the members with box sections are connected by fillet weld. The pinned supports for the two supporting beams are made of bolted joint. TABLE 7.4 Material properties of steel Material

Elastic modulus (kN/m2)

Poisson’s Ratio

Design strength py (kN/m2)

Unit weight (kN/m3)

Q235

2.05 × 108

0.3

2.15 × 105

77

Q345

2.05 × 108

0.3

3.10 × 105

77

Note: 1. All welds must be compatible or over-matching to steel grade used 2. Design strength py for Hot Rolled section and other welded plates

Steel grade Q235 Q345

Thickness less than or equal to (mm)

Design strength py (N/mm2)

16

215

35

205

16

310

35

295

3. For welded section under compression, py should be reduced by 20 N/mm2


267

7.4.2.4.3 Load Combination The basic load cases include dead loads, live loads, wind loads, and temperature loads. The design temperature in Macau is set to be +30/−20°C for unprotected metal structures and +10/−10°C for structures with protection. The wind pressure is obtained from a wind tunnel test due to the complex wind environment and the importance of structure. The wind pressure for wind tunnel test has a return period of 200 years. According to loading code of Macau, the following partial load factors and combinations for the normal ultimate-limit state shall be applied to the strength and stability for normal design situations. Table 7.5 summarizes the partial load factors and combination.

7.4.2.5 Boundary Conditions

All supports are pinned to the concrete beams and columns because the concrete cannot resist the large moments.


As mentioned above, the modeling for the connections using fillet weld is controversial. For simplicity, only the connections between the secondary purlins and the arch main beams will be discussed here. The original design of this type of connection is assumed as pinned connections. To study the structural behavior more exactly, the assumption of semi-rigid connection is also used. For semi-rigid connections, the stiffnesses of the semi-rigid connection are taken as 617 kNm/ rad and 1360 kNm/rad for minor and major axes, respectively. The values of joint stiffnesses are directly calculated from EI/L of the member, in which E is the Young’s modulus of elasticity of steel, I is the second moment of area, and L is the length of the member. For the other member-to-member connections, fully rigid or ideally pinned are assumed.

7.4.2.7 Imperfections

There are no perfect structures or structures that are free from defects due to initial crookedness and residual stress. Imperfections must therefore be considered when using the second-order analysis and advanced analysis to COPHK (2005). Below is a description of codified consideration for member and for frame imperfections. 7.4.2.7.1 Member imperfections For hot-rolled I-sections, Curves A and B of Table 6.1 in COPHK (2005) are used for major and minor axes, respectively. Thus, member imperfections equal to span/500 and span/400 are assumed, TABLE 7.5 Partial load factors Partial load factors for load type Load combination

1. Dead and imposed 2. Dead and lateral 3. Dead, lateral and imposed

Dead Gk

Imposed Qk

Adverse

Beneficial

Adverse

Beneficial

1.35

1.0

1.5

0

1.35 1.35

1.0 1.0

— 1.5 0.9

— 0

Wind wk

Temperature Tk

—

0.9

1.5

—

—

1.5

1.0

0.9

1.5

0.9

268


respectively. For other types of profiled steel section, a larger imperfection may be used and the values of these member types can be found by curve-fitting of buckling experimental curves or design curves from any other codes. Note that direct measurement of member imperfection is not usable here. 7.4.2.7.2 Frame Imperfections The out-of-plumbness equal to the height/200 to COPHK (2005) is assumed. For domes, the frame imperfection can also be taken as span/200 in accordance with the Chinese Technical Specification for latticed shells (JGJ61-2003).

7.4.2.8 Additional Vibration Frequency

According to clause 7.6 of the Code of Practice on Wind Effects in Hong Kong 2004 (HKWC 2004), the natural frequency should be greater than 0.2 Hz for no resonance with wind action. The period of the whole dome frame is found to be 0.57 of a second (i.e., 1.74 Hz) and therefore it is acceptable.

7.4.2.9 Load Carrying Capacity

For the pinned connections case, the maximum section capacity factors are 0.874 and 0.818 for the arch main beams and the secondary purlins, respectively. The section capacity factor is determined from the Equation 7.1. When this factor is greater than 1.0, it means the member will fail under the load combination. For the semi-rigid connections case, the maximum section capacity factors are 0.873 and 0.643 for the arch main beams and the secondary purlins, respectively. As noted above, the modeling for the connections between the arch main beams and the secondary purlins will not affect the arch main beams. However, the maximum section capacity factor of the secondary purlins for the semi-rigid case is 0.175 smaller than that of a pinned connection case. Therefore, about a 20 percent reduction in strength for the secondary purlins can be made when considering the semi-rigid connection.

7.5 Conclusions The direct or second-order analysis allowing for semi-rigid connections is adopted for the design of two dome structures in Hong Kong and Macau. Consideration to code recommendations for local member and global frame imperfections is made to account for geometric and material imperfections. Two types of analysis and design have been used, namely as design check by the Newton-Raphson method and the collapse analysis by the incremental-iterative elastic-plastic analysis. From the examples studied in this chapter, semi-rigid connections combines the benefit of using pinned and rigid connections in which structural stiffness is increased when compared to pinned structures, whereas the transferred moment through connections can be reduced when compared with rigid connections. Most importantly, the analysis and design represent a close reflection of the actual response of the structure, which is basically made of semi-rigid connections as no connections are ideally rigid or perfectly pinned.

References BS 5950-1, Structural use of steelwork in buildings, Code of practice for design—Rolled and welded sections, British Standards Institution, 2000.


269

CEN, Eurocode 3, Design of steel structures, Part1-1: General rules and rules for buildings, EN 1993-1-1, European Committee for Standardization, Brussels, Belgium, 2005. Chan, S. L. and Zhou, Z. H., 2nd-order elastic analysis of frames using single imperfect element per member, Journal of Structural Engineering, ACSE, 121(6), 939–945, 1995. Chan, S. L. and Zhou, Z. H., Elastoplastic and large deflection analysis of steel frames by one element per member II: Three hinges along member, Journal of Structural Engineering, ASCE, 130(4), 545–553, 2004. COPHK, Code of Practice for the Structural Use of Steel 2005, Buildings Department, Hong Kong SAR Government, 2005. Hetao, H. and Li, G., Modified elastic approach for stability design of in-plane frame columns, Advanced Steel Construction, 5(1), 33–48, 2009. HKWC, Code of practice on wind effects in Hong Kong 2004, Buildings Department, Hong Kong SAR Government, 2004. JGJ61-2003, Technical specification for latticed shells, Chinese Planning Press, Beijing (Chinese). Liew, J. Y. R., Chen, H., and Chen W. F., Second-order refined plastic hinge analysis of frame design Parts 1 and 2, Journal of Structural Engineering, ASCE, 119(11), 3196–3216, 1993. NIDA, User’s Manual, Nonlinear Integrated Design and Analysis, NIDA 8.0 HTML Online Documentation, (http://www.nida-naf.com), 2008. White, D. W. and Hajjar, J. F., Stability of steel frames: the cases for simple elastic and rigorous inelastic analysis/design procedures, Engineering Structures, 22(2), 155–167, 2000. Zhou, Z. H. and Chan, S. L., A self-equilibrium element for second-order analysis of semi-rigid jointed frames, Journal of Engineering Mechanics, ASCE, 121(8), 896–902, 1995

: :

© 2011 J. Ross Publishing, Inc.

1) 2)

lu = gc = pc =

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 2

ta = 0.2500" cl = 1.2500" nc = 1 X 2

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 14.10 37.02 27 14.44 39.24 28 14.77 41.46 29 15.12 43.50 30 15.46 45.55 31 15.49 47.36 32 15.51 49.18

Connection subject to pure moment. Hardened washers installed in both legs

5.5000" 2.2500" 3.0000"

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 0.74 1.38 3 1.49 2.76 4 1.93 3.60 5 2.38 4.44 6 2.82 5.28 7 3.27 6.12 8 3.69 7.23 9 4.11 8.34 10 4.70 9.58 11 5.28 10.82 12 5.84 12.40 13 6.39 13.98 14 7.06 15.66 15 7.72 17.34 16 8.38 19.02 17 8.94 20.59 18 9.49 22.16 19 10.05 23.72 20 10.73 25.16 21 11.42 26.59 22 12.10 28.02 23 12.61 30.17 24 13.12 32.32 25 13.61 34.67 ------------------------------

Remark

lp = gb = pb =

Canada Fasteners: A325- -3/4"D 13/16" Oversize holes Material : A36 Fy = -ksi Fu = -ksi

Major parameters

S.L.Lipson (1968) AA-2/1

Column : -Beam : W21X62 Angle : 4 X 3.5 X 1/4

Tested by Test Id.

Connection type : Single web-angle connections Mode : All bolted

I -

1

0

2

4

6

8

10

12

14

16

18

20

0

8

ta

column

24

beam

pc pc pc pc qc

gc

32

40

48

56

64

72

Material : A36 Fy = 36.00 ksi (nominal) : Experimental : Polynominal : M. Exponential : Power model, n = 0.73


Rotation ( x 1/1000 radians )

16

gb

80

A.1 – 1

Semi-rigid Connections Handbook A1–1

Moment ( kip-inch )

R t A3 P3

= Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.250000" = 1.510000 K = 0.239361 = 5 Q1 = 0 Q2 =

( R : X 1/1000 radians )

-6

Q3 =


Bm = ( Rki X R ) / ( 1 + ( R/R0 )**rn )**( 1/rn ) rki = 0.11095362E+01 rmu = 0.28735590E+02

0.47015516E+03

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5397E+00 0.9761E+00 0.6272E+00 0.1110E+01 2 1.38 0.74 1.35 0.76 1.31 0.5397E+00 0.9761E+00 0.5196E+00 0.8535E+00 3 2.76 1.49 2.69 1.48 2.40 0.5335E+00 0.9761E+00 0.5311E+00 0.7284E+00 4 3.60 1.93 3.51 1.93 2.99 0.5298E+00 0.9761E+00 0.5326E+00 0.6715E+00 5 4.44 2.38 4.33 2.37 3.53 0.5298E+00 0.9761E+00 0.5230E+00 0.6237E+00 6 5.28 2.82 5.15 2.81 4.04 0.5298E+00 0.9761E+00 0.5045E+00 0.5826E+00 7 6.12 3.27 5.97 3.22 4.51 0.4659E+00 0.9761E+00 0.4810E+00 0.5468E+00 8 7.23 3.69 7.05 3.73 5.09 0.3818E+00 0.9761E+00 0.4484E+00 0.5058E+00 9 8.34 4.11 8.14 4.22 5.63 0.4230E+00 0.9761E+00 0.4195E+00 0.4705E+00 10 9.58 4.70 9.35 4.72 6.20 0.4693E+00 0.9761E+00 0.3952E+00 0.4361E+00 11 10.82 5.28 10.56 5.20 6.72 0.4177E+00 0.9761E+00 0.3802E+00 0.4063E+00 12 12.40 5.84 12.10 5.80 7.33 0.3523E+00 0.9761E+00 0.3728E+00 0.3735E+00 13 13.98 6.39 13.65 6.38 7.90 0.3725E+00 0.9761E+00 0.3745E+00 0.3452E+00 14 15.66 7.06 15.29 7.03 8.46 0.3941E+00 0.9761E+00 0.3900E+00 0.3192E+00 15 17.34 7.72 16.93 7.69 8.98 0.3941E+00 0.9761E+00 0.3966E+00 0.2965E+00 16 19.02 8.38 18.57 8.36 9.46 0.3740E+00 0.9761E+00 0.4004E+00 0.2766E+00 17 20.59 8.94 20.10 8.99 9.88 0.3553E+00 0.9761E+00 0.3999E+00 0.2600E+00 18 22.16 9.49 21.63 9.62 10.27 0.3554E+00 0.9761E+00 0.3950E+00 0.2451E+00 19 23.72 10.05 23.16 10.23 10.65 0.4182E+00 0.9761E+00 0.3857E+00 0.2316E+00 20 25.16 10.73 24.56 10.77 10.97 0.4757E+00 0.9761E+00 0.3738E+00 0.2204E+00 21 26.59 11.42 25.96 11.30 11.28 0.4757E+00 0.9761E+00 0.3592E+00 0.2100E+00 22 28.02 12.10 27.35 11.80 11.57 0.3802E+00 0.9761E+00 0.3423E+00 0.2005E+00 23 30.17 12.61 29.45 12.51 11.99 0.2372E+00 0.9761E+00 0.3143E+00 0.1876E+00 24 32.32 13.12 31.55 13.15 12.38 0.2241E+00 0.9761E+00 0.2485E+00 0.1760E+00 25 34.67 13.61 33.84 13.70 12.78 0.2098E+00 0.9761E+00 0.2155E+00 0.1647E+00 26 37.02 14.10 36.14 14.17 13.16 0.1792E+00 0.9760E+00 0.1836E+00 0.1546E+00 27 39.24 14.44 38.30 14.54 13.49 0.1503E+00 0.9760E+00 0.1553E+00 0.1460E+00 28 41.46 14.77 40.46 14.86 13.80 0.1601E+00 0.9760E+00 0.1295E+00 0.1381E+00 29 43.50 15.12 42.46 15.10 14.08 0.1693E+00 0.9760E+00 0.1079E+00 0.1315E+00 30 45.55 15.46 44.46 15.30 14.34 0.8635E-01 0.9760E+00 0.8853E-01 0.1254E+00 31 47.36 15.49 46.23 15.45 14.57 0.1294E-01 0.9760E+00 0.7328E-01 0.1204E+00 32 49.18 15.51 48.00 15.57 14.78 0.1291E-01 0.9760E+00 0.5972E-01 0.1157E+00 ----------------------------------------------------------------------------------------------------------------------------

Power model : rn = 0.731

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.75435250E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.29149749E+01 -0.29963328E+02 0.73967184E+01 0.37852066E+03 -0.81221006E+03 Rj0 = 13.9800 32.3200 RKj = 0.92425571E-02 -0.35940357E-01

Frye and Morris polynominal model : xd = 5.500000" g = 2.762500" A1 = 4.280000 A2 = 1.450000 P1 = 1 P2 = 3


A.1 – 2

A1–2 Semi-rigid Connections Handbook

: :


1) 2)

lu = gc = pc =

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 2

ta = 0.2500" cl = 1.2500" nc = 1 X 2

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 15.04 25.71 27 15.19 26.77 28 15.33 27.82 29 15.47 28.87 30 16.22 30.19 31 16.97 31.50


5.5000" 2.2500" 3.0000"


Remark

lp = gb = pb =


Major parameters



Tested by Test Id.


I -

2

0

3

6

9

12

15

18

21

24

27

30

0

gb lu cu pb pb pb lp pb cl qb ll beam

5

15

20

25

30


10

qc

35

pc pc pc pc


ta

column

40

gc

45

50

A.1 – 3


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.16063551E+04

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.7224E+00 0.9761E+00 -0.7311E+00 0.1110E+01 2 0.64 0.46 0.62 0.31 0.69 0.7222E+00 0.9761E+00 0.1100E+01 0.1054E+01 3 1.28 0.92 1.25 1.01 1.35 0.7017E+00 0.9761E+00 0.9868E+00 0.1004E+01 4 2.19 1.54 2.14 1.68 2.23 0.6727E+00 0.9761E+00 0.5378E+00 0.9387E+00 5 3.10 2.15 3.02 2.12 3.06 0.6875E+00 0.9761E+00 0.4868E+00 0.8798E+00 6 3.97 2.76 3.88 2.62 3.81 0.7017E+00 0.9761E+00 0.6595E+00 0.8283E+00 7 4.85 3.38 4.73 3.28 4.51 0.7667E+00 0.9761E+00 0.8396E+00 0.7814E+00 8 5.72 4.10 5.59 4.06 5.18 0.8319E+00 0.9761E+00 0.9323E+00 0.7383E+00 9 6.60 4.83 6.44 4.88 5.80 0.8319E+00 0.9761E+00 0.9275E+00 0.6988E+00 10 7.48 5.56 7.30 5.66 6.40 0.7763E+00 0.9761E+00 0.8530E+00 0.6624E+00 11 8.33 6.18 8.13 6.35 6.95 0.7222E+00 0.9761E+00 0.7475E+00 0.6297E+00 12 9.18 6.79 8.96 6.94 7.47 0.7222E+00 0.9761E+00 0.6368E+00 0.5993E+00 13 10.03 7.41 9.79 7.44 7.97 0.6651E+00 0.9761E+00 0.5387E+00 0.5711E+00 14 11.04 8.01 10.78 7.94 8.53 0.5975E+00 0.9761E+00 0.4503E+00 0.5403E+00 15 12.05 8.62 11.77 8.41 9.07 0.5974E+00 0.9761E+00 0.4867E+00 0.5119E+00 16 13.06 9.22 12.75 8.89 9.57 0.4661E+00 0.9761E+00 0.4592E+00 0.4857E+00 17 14.48 9.62 14.13 9.53 10.23 0.2825E+00 0.9761E+00 0.4535E+00 0.4524E+00 18 15.89 10.02 15.51 10.18 10.85 0.3912E+00 0.9761E+00 0.4669E+00 0.4224E+00 19 17.10 10.60 16.69 10.75 11.35 0.4845E+00 0.9761E+00 0.4812E+00 0.3990E+00 20 18.31 11.19 17.87 11.34 11.82 0.4845E+00 0.9761E+00 0.4911E+00 0.3775E+00 21 19.52 11.78 19.06 11.94 12.26 0.5295E+00 0.9761E+00 0.4933E+00 0.3577E+00 22 20.58 12.38 20.08 12.45 12.63 0.5686E+00 0.9761E+00 0.4882E+00 0.3417E+00 23 21.63 12.98 21.11 12.96 12.98 0.5686E+00 0.9761E+00 0.4770E+00 0.3267E+00 24 22.69 13.58 22.14 13.46 13.32 0.5340E+00 0.9761E+00 0.4604E+00 0.3128E+00 25 24.20 14.31 23.62 14.13 13.78 0.4845E+00 0.9761E+00 0.4298E+00 0.2942E+00 26 25.71 15.04 25.10 14.76 14.21 0.2786E+00 0.9761E+00 0.3941E+00 0.2773E+00 27 26.77 15.19 26.13 15.16 14.50 0.1354E+00 0.9761E+00 0.3680E+00 0.2664E+00 28 27.82 15.33 27.16 15.53 14.77 0.1354E+00 0.9761E+00 0.3418E+00 0.2561E+00 29 28.87 15.47 28.18 15.88 15.04 0.3295E+00 0.9761E+00 0.3163E+00 0.2464E+00 30 30.19 16.22 29.46 16.27 15.35 0.5714E+00 0.9761E+00 0.2860E+00 0.2351E+00 31 31.50 16.97 30.75 16.63 15.65 0.5714E+00 0.9761E+00 0.2581E+00 0.2245E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.42240750E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.25526455E+02 0.37619342E+03 -0.18708504E+04 0.41350051E+04 -0.42052409E+04 Rj0 = 11.5000 RKj = 0.92198278E-01



A.1 – 4


: :


1) 2)

lu = gc = pc =

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 3

ta = 0.2500" cl = 1.2500" nc = 1 X 3

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 43.73 37.17 27 44.43 39.21 28 45.47 41.30 29 46.52 43.38 30 47.59 45.12 31 48.66 46.87 32 49.35 49.02 33 50.05 51.16


8.5000" 2.2500" 3.0000"


Remark

lp = gb = pb =


Major parameters



Tested by Test Id.


I -

3

0

10

20

30

40

50

60

70

80

90

100

0


8

24

32

40

48


16

qc

56

pc pc pc pc


ta

column

64

gc

72

80

A.1 – 5


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



-0.78091338E+03

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2131E+01 0.2775E+01 0.1141E+01 0.3441E+01 2 1.01 2.16 2.81 1.91 3.29 0.2131E+01 0.2775E+01 0.2363E+01 0.3079E+01 3 2.02 4.31 5.62 4.44 6.25 0.2305E+01 0.2775E+01 0.2543E+01 0.2784E+01 4 2.97 6.65 8.24 6.80 8.77 0.2468E+01 0.2775E+01 0.2416E+01 0.2549E+01 5 3.91 8.98 10.86 9.00 11.08 0.2321E+01 0.2775E+01 0.2240E+01 0.2344E+01 6 4.99 11.30 13.86 11.32 13.50 0.2152E+01 0.2775E+01 0.2076E+01 0.2141E+01 7 6.07 13.63 16.85 13.50 15.71 0.2013E+01 0.2775E+01 0.1965E+01 0.1964E+01 8 7.32 15.94 20.31 15.89 18.05 0.1853E+01 0.2775E+01 0.1883E+01 0.1786E+01 9 8.57 18.25 23.77 18.20 20.18 0.1823E+01 0.2775E+01 0.1819E+01 0.1633E+01 10 9.95 20.72 27.61 20.66 22.33 0.1789E+01 0.2775E+01 0.1743E+01 0.1485E+01 11 11.33 23.19 31.44 23.01 24.29 0.1603E+01 0.2775E+01 0.1647E+01 0.1357E+01 12 12.71 25.15 35.27 25.20 26.08 0.1418E+01 0.2775E+01 0.1528E+01 0.1246E+01 13 14.09 27.10 39.10 27.22 27.73 0.1289E+01 0.2775E+01 0.1390E+01 0.1148E+01 14 15.64 28.88 43.39 29.24 29.43 0.1145E+01 0.2775E+01 0.1221E+01 0.1051E+01 15 17.18 30.65 47.68 30.99 30.99 0.1059E+01 0.2775E+01 0.1047E+01 0.9665E+00 16 18.83 32.24 52.25 32.57 32.52 0.9668E+00 0.2775E+01 0.8653E+00 0.8873E+00 17 20.48 33.83 56.83 33.85 33.92 0.9668E+00 0.2775E+01 0.6961E+00 0.8176E+00 18 22.13 35.42 61.40 34.87 35.22 0.9668E+00 0.2775E+01 0.5442E+00 0.7559E+00 19 23.77 37.02 65.97 35.79 36.41 0.6920E+00 0.2775E+01 0.9060E+00 0.7011E+00 20 25.69 37.73 71.27 37.39 37.70 0.3728E+00 0.2775E+01 0.7782E+00 0.6447E+00 21 27.60 38.44 76.58 38.78 38.89 0.4739E+00 0.2775E+01 0.6767E+00 0.5949E+00 22 29.68 39.66 82.36 40.10 40.07 0.5840E+00 0.2775E+01 0.5927E+00 0.5471E+00 23 31.76 40.87 88.13 41.27 41.17 0.6149E+00 0.2775E+01 0.5322E+00 0.5049E+00 24 33.44 41.95 92.79 42.13 41.99 0.6399E+00 0.2775E+01 0.4972E+00 0.4743E+00 25 35.12 43.02 97.45 42.94 42.76 0.5063E+00 0.2775E+01 0.4723E+00 0.4465E+00 26 37.17 43.73 103.13 43.89 43.64 0.3434E+00 0.2775E+01 0.4526E+00 0.4158E+00 27 39.21 44.43 108.81 44.80 44.47 0.4218E+00 0.2775E+01 0.4417E+00 0.3882E+00 28 41.30 45.47 114.59 45.71 45.25 0.5015E+00 0.2775E+01 0.4370E+00 0.3629E+00 29 43.38 46.52 120.36 46.62 45.98 0.5619E+00 0.2775E+01 0.4367E+00 0.3400E+00 30 45.12 47.59 125.20 47.39 46.56 0.6125E+00 0.2775E+01 0.4387E+00 0.3224E+00 31 46.87 48.66 130.05 48.15 47.10 0.4830E+00 0.2775E+01 0.4420E+00 0.3062E+00 32 49.02 49.35 136.01 49.11 47.74 0.3237E+00 0.2774E+01 0.4470E+00 0.2879E+00 33 51.16 50.05 141.97 50.07 48.34 0.3237E+00 0.2774E+01 0.4525E+00 0.2712E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.67934167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.96571609E+01 -0.29073652E+01 0.47525019E+03 -0.17286658E+04 0.20828160E+04 Rj0 = 23.5000 RKj = 0.49381954E+00



A.1 – 6


: :


1) 2)

lu = gc = pc =

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 3

ta = 0.2500" cl = 1.2500" nc = 1 X 3

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 44.60 17.74 27 46.25 18.52 28 47.90 19.40 29 49.55 20.28


8.5000" 2.2500" 3.0000"


Remark

lp = gb = pb =


Major parameters



Tested by Test Id.


I -

4

0

10

20

30

40

50

60

70

80

90

100

0


4

12

16

20

24


8

qc

28

pc pc pc pc


ta

column

32

gc

36

40

A.1 – 7


Moment ( kip-inch )

R t A3 P3

( R : X 1/1000 radians ) = Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.250000" = 1.510000 K = 0.084201 = 5 Q1 = 0 Q2 = -6

Q3 =



0.24586727E+03

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3067E+01 0.2775E+01 0.2094E+01 0.3441E+01 2 0.65 2.01 1.82 2.06 2.25 0.3067E+01 0.2775E+01 0.2977E+01 0.3431E+01 3 1.31 4.01 3.63 3.99 4.49 0.3067E+01 0.2775E+01 0.2967E+01 0.3404E+01 4 1.96 6.02 5.45 5.97 6.70 0.3119E+01 0.2775E+01 0.3113E+01 0.3363E+01 5 2.53 7.81 7.02 7.77 8.59 0.3163E+01 0.2775E+01 0.3236E+01 0.3319E+01 6 3.09 9.59 8.58 9.62 10.45 0.3163E+01 0.2775E+01 0.3305E+01 0.3267E+01 7 3.66 11.38 10.15 11.49 12.28 0.3228E+01 0.2775E+01 0.3306E+01 0.3209E+01 8 4.27 13.39 11.84 13.48 14.21 0.3297E+01 0.2775E+01 0.3239E+01 0.3139E+01 9 4.88 15.40 13.53 15.43 16.11 0.3297E+01 0.2775E+01 0.3119E+01 0.3064E+01 10 5.49 17.41 15.23 17.28 17.95 0.3019E+01 0.2775E+01 0.2966E+01 0.2984E+01 11 6.14 19.19 17.04 19.16 19.87 0.2720E+01 0.2775E+01 0.2784E+01 0.2894E+01 12 6.79 20.97 18.85 20.92 21.73 0.2720E+01 0.2775E+01 0.2602E+01 0.2801E+01 13 7.45 22.75 20.67 22.57 23.54 0.2581E+01 0.2775E+01 0.2428E+01 0.2706E+01 14 8.43 25.07 23.39 25.02 26.12 0.2373E+01 0.2775E+01 0.2639E+01 0.2561E+01 15 9.41 27.40 26.11 27.51 28.55 0.2282E+01 0.2775E+01 0.2451E+01 0.2416E+01 16 10.11 28.95 28.04 29.18 30.21 0.2216E+01 0.2775E+01 0.2342E+01 0.2314E+01 17 10.80 30.49 29.98 30.78 31.79 0.2216E+01 0.2775E+01 0.2252E+01 0.2214E+01 18 11.50 32.04 31.92 32.33 33.30 0.2371E+01 0.2775E+01 0.2177E+01 0.2115E+01 19 12.25 33.93 33.98 33.92 34.83 0.2536E+01 0.2775E+01 0.2111E+01 0.2013E+01 20 12.99 35.81 36.05 35.47 36.29 0.2536E+01 0.2775E+01 0.2058E+01 0.1914E+01 21 13.73 37.70 38.11 36.99 37.68 0.2029E+01 0.2775E+01 0.2014E+01 0.1819E+01 22 14.54 38.90 40.35 38.60 39.11 0.1478E+01 0.2775E+01 0.1975E+01 0.1720E+01 23 15.35 40.09 42.60 40.18 40.46 0.1478E+01 0.2775E+01 0.1942E+01 0.1625E+01 24 16.16 41.29 44.84 41.74 41.74 0.1793E+01 0.2775E+01 0.1915E+01 0.1535E+01 25 16.95 42.94 47.03 43.24 42.92 0.2100E+01 0.2775E+01 0.1893E+01 0.1452E+01 26 17.74 44.60 49.21 44.73 44.03 0.2100E+01 0.2775E+01 0.1874E+01 0.1373E+01 27 18.52 46.25 51.40 46.20 45.08 0.1995E+01 0.2775E+01 0.1857E+01 0.1298E+01 28 19.40 47.90 53.83 47.82 46.18 0.1878E+01 0.2775E+01 0.1841E+01 0.1220E+01 29 20.28 49.55 56.27 49.43 47.22 0.1878E+01 0.2775E+01 0.1827E+01 0.1147E+01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.33263667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.15457230E+01 0.60249888E+02 -0.31690963E+03 0.62739613E+03 -0.59688369E+03 Rj0 = 0.0000 8.0000 RKj = 0.12980867E+01 0.44060924E+00



A.1 – 8


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.2500" cl = 1.2500" nc = 1 X 4

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 70.13 27.00 27 71.76 28.73 28 73.39 30.53 29 75.02 32.34 30 76.58 34.17 31 78.15 36.01 32 79.57 37.94 33 81.00 39.87 34 82.36 41.87 35 83.72 43.87 36 84.81 45.77 37 85.91 47.67 38 87.33 49.54 39 88.76 51.41 40 90.57 54.41 41 92.11 57.01 42 93.55 58.28 43 94.84 60.41


lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters



Tested by Test Id.


I -

5

0

15

30

45

60

75

90

105

120

135

150

0

10

ta

column

30

beam

pc pc pc pc qc

gc

40

50

60

70

80

90

100




20

gb

A.1 – 9


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.59070956E+03

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4072E+01 0.5732E+01 0.2570E+01 0.7992E+01 3 1.39 6.10 7.98 6.10 9.68 0.4814E+01 0.5732E+01 0.5343E+01 0.6170E+01 5 2.38 11.48 13.66 11.49 15.38 0.6292E+01 0.5732E+01 0.5425E+01 0.5378E+01 7 3.61 18.05 20.70 17.93 21.51 0.4614E+01 0.5732E+01 0.5007E+01 0.4634E+01 9 5.24 25.41 30.05 25.57 28.44 0.4990E+01 0.5732E+01 0.4375E+01 0.3897E+01 11 6.47 30.78 37.06 30.66 32.93 0.3912E+01 0.5732E+01 0.3970E+01 0.3468E+01 13 8.09 36.74 46.37 36.72 38.18 0.3498E+01 0.5732E+01 0.3492E+01 0.3011E+01 15 9.95 42.63 57.02 42.73 43.37 0.2835E+01 0.5732E+01 0.2980E+01 0.2600E+01 17 11.83 47.72 67.83 47.87 47.95 0.2573E+01 0.5732E+01 0.2481E+01 0.2271E+01 19 14.12 52.67 80.92 52.89 52.76 0.1864E+01 0.5732E+01 0.1924E+01 0.1955E+01 21 18.37 59.85 105.31 59.25 60.11 0.1427E+01 0.5732E+01 0.1737E+01 0.1527E+01 23 21.85 64.44 125.25 64.50 64.97 0.1255E+01 0.5732E+01 0.1317E+01 0.1279E+01 25 25.26 68.50 144.79 68.52 69.00 0.1067E+01 0.5732E+01 0.1064E+01 0.1093E+01 27 28.73 71.76 164.68 71.93 72.53 0.9220E+00 0.5732E+01 0.9123E+00 0.9445E+00 29 32.34 75.02 185.34 75.04 75.71 0.8778E+00 0.5732E+01 0.8198E+00 0.8214E+00 31 36.01 78.15 206.38 77.94 78.53 0.7959E+00 0.5732E+01 0.7629E+00 0.7203E+00 33 39.87 81.00 228.55 80.81 81.14 0.7090E+00 0.5732E+01 0.7240E+00 0.6335E+00 35 43.87 83.72 251.48 83.64 83.52 0.6264E+00 0.5731E+01 0.6961E+00 0.5598E+00 37 47.67 85.91 273.25 86.25 85.54 0.6712E+00 0.5731E+01 0.6765E+00 0.5017E+00 39 51.41 88.76 294.66 88.75 87.32 0.7021E+00 0.5731E+01 0.6617E+00 0.4532E+00 41 57.01 92.11 326.74 92.40 89.68 0.9573E+00 0.5731E+01 0.6456E+00 0.3932E+00 43 60.41 94.84 346.24 94.59 90.96 0.6046E+00 0.5731E+01 0.6387E+00 0.3625E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.70688417E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.25968016E+02 0.24808235E+03 -0.10304382E+04 0.18661063E+04 -0.15796917E+04 Rj0 = 18.3700 RKj = 0.61845541E+00



A.1 – 10


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.2500" cl = 1.2500" nc = 1 X 4

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 76.56 22.75 27 78.28 24.05 28 79.99 25.35 29 81.84 26.75 30 83.69 28.15 31 85.73 29.95 32 87.77 31.75 33 89.54 33.42 34 91.32 35.08 35 93.16 37.01 36 95.00 38.94 37 96.71 40.71 38 98.42 42.47 39 100.19 44.47 40 101.96 46.47 41 103.34 48.06 42 104.71 49.66


lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters



Tested by Test Id.


I -

6

0

15

30

45

60

75

90

105

120

135

150

0

8

ta

column

24

beam

pc pc pc pc qc

gc

32

40

48

56

64

72




16

gb

80

A.1 – 11


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.58384858E+03

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.8351E+01 0.5732E+01 0.7418E+01 0.7992E+01 3 0.75 6.65 4.31 6.60 5.82 0.9698E+01 0.5732E+01 0.9322E+01 0.7473E+01 5 1.57 14.10 9.02 13.92 11.72 0.7849E+01 0.5732E+01 0.8266E+01 0.6895E+01 7 2.39 19.95 13.69 20.02 17.12 0.6499E+01 0.5732E+01 0.6707E+01 0.6360E+01 9 3.54 26.33 20.28 26.73 24.04 0.5737E+01 0.5732E+01 0.5119E+01 0.5684E+01 11 4.49 31.91 25.72 31.21 29.18 0.5055E+01 0.5732E+01 0.4425E+01 0.5192E+01 13 6.03 37.62 34.57 37.61 36.66 0.3634E+01 0.5732E+01 0.3939E+01 0.4502E+01 15 8.52 47.18 48.83 46.87 46.72 0.3543E+01 0.5732E+01 0.3490E+01 0.3629E+01 17 10.33 52.75 59.21 52.80 52.83 0.2826E+01 0.5732E+01 0.3045E+01 0.3135E+01 19 12.54 58.32 71.87 58.84 59.20 0.2512E+01 0.5732E+01 0.2419E+01 0.2652E+01 21 14.81 64.02 84.91 63.64 64.76 0.2130E+01 0.5732E+01 0.1814E+01 0.2257E+01 23 17.68 68.77 101.36 67.94 70.66 0.1658E+01 0.5732E+01 0.2093E+01 0.1869E+01 25 21.45 74.72 122.97 74.79 76.95 0.1421E+01 0.5732E+01 0.1587E+01 0.1491E+01 27 24.05 78.28 137.88 78.61 80.56 0.1319E+01 0.5732E+01 0.1372E+01 0.1291E+01 29 26.75 81.84 153.35 82.10 83.81 0.1319E+01 0.5732E+01 0.1223E+01 0.1122E+01 31 29.95 85.73 171.68 85.81 87.13 0.1135E+01 0.5732E+01 0.1107E+01 0.9610E+00 33 33.42 89.54 191.54 89.50 90.21 0.1067E+01 0.5732E+01 0.1027E+01 0.8217E+00 35 37.01 93.16 212.15 93.09 92.95 0.9526E+00 0.5732E+01 0.9741E+00 0.7062E+00 37 40.71 96.71 233.33 96.62 95.38 0.9681E+00 0.5731E+01 0.9391E+00 0.6106E+00 39 44.47 100.19 254.89 100.11 97.52 0.8872E+00 0.5731E+01 0.9163E+00 0.5315E+00 41 48.06 103.34 275.49 103.38 99.32 0.8623E+00 0.5731E+01 0.9025E+00 0.4692E+00 ----------------------------------------------------------------------------------------------------------------------------





A.1 – 12


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 5

ta = 0.2500" cl = 1.2500" nc = 1 X 5

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 156.20 23.02 27 160.17 24.58 28 164.82 26.30 29 169.46 28.02 30 173.85 30.08 31 178.23 32.14 32 181.91 34.36 33 185.59 36.59 34 187.89 38.16 35 190.18 39.73 36 192.48 41.31 37 194.84 42.89 38 197.21 44.47 39 199.38 45.82 40 201.54 47.17


lu = gc = pc =


Remark

lp = 14.5000" gb = 2.2500" pb = 3.0000"


Major parameters



Tested by Test Id.


I -

7

0

25

50

75

100

125

150

175

200

225

250

0

8

ta

column

24

beam

pc pc pc pc qc

gc

32

40

48

56

64

72




16

gb

80

A.1 – 13


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.33823696E+04

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1344E+02 0.9998E+01 0.1487E+02 0.1554E+02 3 1.10 14.85 11.05 14.60 16.95 0.1344E+02 0.9998E+01 0.1306E+02 0.1502E+02 5 2.18 29.09 21.75 29.32 32.55 0.1317E+02 0.9998E+01 0.1435E+02 0.1410E+02 7 3.14 43.18 31.43 43.33 45.74 0.1613E+02 0.9998E+01 0.1435E+02 0.1311E+02 9 4.11 57.05 41.12 56.75 57.94 0.1274E+02 0.9998E+01 0.1323E+02 0.1207E+02 11 5.28 70.90 52.82 71.06 71.33 0.1112E+02 0.9998E+01 0.1118E+02 0.1082E+02 13 6.59 83.82 65.84 84.11 84.56 0.8712E+01 0.9998E+01 0.8898E+01 0.9513E+01 15 8.05 95.13 80.51 95.60 97.53 0.6904E+01 0.9998E+01 0.6891E+01 0.8184E+01 17 9.75 105.95 97.52 105.96 110.29 0.5861E+01 0.9998E+01 0.5426E+01 0.6859E+01 19 12.74 120.09 127.37 120.20 127.92 0.4315E+01 0.9998E+01 0.4321E+01 0.5055E+01 21 15.11 130.39 151.09 129.99 138.61 0.4010E+01 0.9998E+01 0.3967E+01 0.4005E+01 23 17.95 140.66 179.51 140.75 148.60 0.3467E+01 0.9998E+01 0.3591E+01 0.3075E+01 25 21.47 152.23 214.67 152.37 157.91 0.2901E+01 0.9998E+01 0.2992E+01 0.2270E+01 27 24.58 160.17 245.73 160.74 164.14 0.2623E+01 0.9998E+01 0.2396E+01 0.1771E+01 29 28.02 169.46 280.17 167.90 169.52 0.2438E+01 0.9998E+01 0.2725E+01 0.1374E+01 31 32.14 178.23 321.33 177.81 174.45 0.1902E+01 0.9997E+01 0.2117E+01 0.1039E+01 33 36.59 185.59 365.81 186.13 178.48 0.1540E+01 0.9997E+01 0.1654E+01 0.7899E+00 35 39.73 190.18 397.25 190.96 180.75 0.1459E+01 0.9997E+01 0.1431E+01 0.6601E+00 37 42.89 194.84 428.80 195.21 182.67 0.1496E+01 0.9997E+01 0.1273E+01 0.5573E+00 39 45.82 199.38 458.11 198.78 184.19 0.1604E+01 0.9997E+01 0.1171E+01 0.4802E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.53120333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.59232979E+02 -0.56866471E+03 0.73074258E+03 0.23528880E+04 -0.57731910E+04 Rj0 = 28.0200 RKj = 0.95351928E+00



A.1 – 14


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 5

ta = 0.2500" cl = 1.2500" nc = 1 X 5

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 170.52 17.35 27 175.42 18.64 28 178.84 19.58 29 182.26 20.53 30 185.67 21.48 31 190.12 22.86 32 194.56 24.25 33 197.87 25.43 34 201.19 26.61 35 203.18 27.32 36 205.17 28.03


lu = gc = pc =


Remark

lp = 14.5000" gb = 2.2500" pb = 3.0000"


Major parameters



Tested by Test Id.


I -

8

0

25

50

75

100

125

150

175

200

225

250

0

5

ta

column

15

beam

pc pc pc pc qc

gc

20

25

30

35

40

45




10

gb

50

A.1 – 15


Moment ( kip-inch )

R t A3 P3


Q3 =



0.58129608E+04

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2305E+02 0.9998E+01 0.2272E+02 0.1554E+02 3 0.66 15.21 6.59 15.45 10.25 0.2305E+02 0.9998E+01 0.2278E+02 0.1554E+02 5 1.38 30.79 13.76 30.65 21.37 0.2064E+02 0.9998E+01 0.1977E+02 0.1551E+02 7 2.21 46.05 22.14 46.24 34.35 0.1611E+02 0.9998E+01 0.1764E+02 0.1541E+02 9 3.12 61.31 31.20 61.56 48.22 0.1757E+02 0.9998E+01 0.1625E+02 0.1519E+02 11 4.06 76.11 40.58 76.12 62.31 0.1408E+02 0.9998E+01 0.1473E+02 0.1481E+02 13 5.03 89.07 50.26 89.51 76.38 0.1270E+02 0.9998E+01 0.1291E+02 0.1424E+02 15 6.10 102.70 60.95 102.24 91.18 0.1278E+02 0.9998E+01 0.1091E+02 0.1339E+02 17 7.47 115.62 74.66 115.67 108.63 0.6915E+01 0.9998E+01 0.8792E+01 0.1203E+02 19 9.55 130.99 95.46 131.59 131.20 0.7041E+01 0.9998E+01 0.6705E+01 0.9640E+01 21 11.25 142.27 112.48 142.04 145.95 0.5878E+01 0.9998E+01 0.5632E+01 0.7712E+01 23 13.56 153.49 135.54 153.69 161.06 0.4847E+01 0.9998E+01 0.4498E+01 0.5484E+01 25 16.07 165.61 160.63 163.56 172.45 0.4329E+01 0.9998E+01 0.3383E+01 0.3699E+01 27 18.64 175.42 186.34 175.71 180.27 0.3697E+01 0.9998E+01 0.4235E+01 0.2470E+01 29 20.53 182.26 205.28 183.12 184.33 0.3608E+01 0.9998E+01 0.3619E+01 0.1850E+01 31 22.86 190.12 228.60 190.84 187.98 0.3205E+01 0.9998E+01 0.3030E+01 0.1316E+01 33 25.43 197.87 254.26 198.00 190.82 0.2806E+01 0.9998E+01 0.2577E+01 0.9229E+00 35 27.32 203.18 273.17 202.65 192.36 0.2806E+01 0.9998E+01 0.2350E+01 0.7211E+00 ----------------------------------------------------------------------------------------------------------------------------





A.1 – 16


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 6

ta = 0.2500" cl = 1.2500" nc = 1 X 6

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 237.94 23.45 27 243.96 24.94 28 250.38 26.86 29 256.81 28.79 30 263.01 30.72 31 269.20 32.65 32 274.71 34.64 33 280.21 36.63 34 285.27 38.52 35 290.32 40.41 36 294.49 42.10 37 298.65 43.79 38 306.40 46.19 39 314.14 48.59


lu = gc = pc =


Remark

lp = 17.5000" gb = 2.2500" pb = 3.0000"


Major parameters



Tested by Test Id.


I -

9

0

40

80

120

160

200

240

280

320

360

400

0

8

ta

column

24

beam

pc pc pc pc qc

gc

32

40

48

56

64

72




16

gb

80

A.1 – 17


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.17958368E+04

-13



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.46954583E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.18867636E+02 0.46790588E+02 -0.88864194E+03 0.30074935E+04 -0.37645101E+04 Rj0 = 11.2300 18.6300 24.9400 RKj = 0.21486458E+01 0.84925674E+00 -0.36341194E+00



A.1 – 18


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 6

ta = 0.2500" cl = 1.2500" nc = 1 X 6

------------------------------



lu = gc = pc =


Remark

lp = 17.5000" gb = 2.2500" pb = 3.0000"


Major parameters



Tested by Test Id.


I - 10

0

40

80

120

160

200

240

280

320

360

400

0

6

ta

column

18

beam

pc pc pc pc qc

gc

24

30

36

42

48

54




12

gb

60

A.1 – 19


Moment ( kip-inch )

R t A3 P3


Q3 =



0.68285046E+04

-13



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.38642583E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.14274756E+03 0.19325879E+04 -0.87476896E+04 0.18204321E+05 -0.17815485E+05 Rj0 = 10.6100 18.6700 RKj = 0.30365395E+01 -0.16767093E+00



A.1 – 20


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.3125" cl = 1.2500" nc = 1 X 4

------------------------------



lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters

S.L.Lipson (1968) BB-4/1


Tested by Test Id.


I - 11

0

20

40

60

80

100

120

140

160

180

200

0

10

ta

column

30

beam

pc pc pc pc qc

gc

40

50

60

70

80

90

100




20

gb

A.1 – 21


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



-0.84062951E+03

-13



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.64285167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.45751894E+02 -0.75951420E+03 0.33127018E+04 -0.57815929E+04 0.41378111E+04 Rj0 = 27.8600 42.4600 RKj = 0.64096720E+00 0.12267807E+00



A.1 – 22


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.3125" cl = 1.2500" nc = 1 X 4

------------------------------



lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters

S.L.Lipson (1968) BB-4/2


Tested by Test Id.


I - 12

0

20

40

60

80

100

120

140

160

180

200

0

8

ta

column

24

beam

pc pc pc pc qc

gc

32

40

48

56

64

72




16

gb

80

A.1 – 23


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.34273301E+03

-13



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.49699333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.77717127E+01 -0.40026797E+02 0.33779186E+02 0.55997685E+02 -0.30075810E+03 Rj0 = 13.2800 21.5800 RKj = 0.10031083E+01 0.41204916E+00



A.1 – 24


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.3125" cl = 1.2500" nc = 1 X 4

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 93.22 12.32 27 95.81 13.16 28 98.40 14.00 29 100.12 14.70 30 101.84 15.40 31 103.56 16.24 32 105.28 17.07 33 106.60 17.98 34 107.92 18.88 35 109.33 19.77 36 110.74 20.66 37 112.15 21.54

Connection subject to moment and shear.

lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters

S.L.Lipson (1968) B2-4


Tested by Test Id.


I - 13

0

15

30

45

60

75

90

105

120

135

150

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32

36




8

gb

40

A.1 – 25


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.36438006E+04

-13

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1262E+02 0.8584E+01 0.9974E+01 0.1806E+02 3 0.48 6.12 4.16 5.84 8.20 0.1201E+02 0.8584E+01 0.1320E+02 0.1591E+02 5 1.14 14.31 9.81 14.60 17.92 0.1703E+02 0.8584E+01 0.1306E+02 0.1374E+02 7 1.59 20.63 13.69 20.34 23.86 0.1203E+02 0.8584E+01 0.1228E+02 0.1254E+02 9 2.22 27.61 19.02 27.59 31.19 0.1064E+02 0.8584E+01 0.1109E+02 0.1115E+02 11 2.83 34.13 24.33 34.11 37.73 0.1040E+02 0.8584E+01 0.9983E+01 0.1000E+02 13 3.52 40.39 30.21 40.57 44.20 0.8284E+01 0.8584E+01 0.8948E+01 0.8937E+01 15 4.44 48.03 38.12 48.31 51.87 0.8314E+01 0.8584E+01 0.7926E+01 0.7768E+01 17 5.50 56.28 47.18 56.26 59.49 0.7331E+01 0.8584E+01 0.7178E+01 0.6700E+01 19 6.72 64.79 57.68 64.66 67.07 0.6661E+01 0.8584E+01 0.6581E+01 0.5727E+01 21 8.18 73.90 70.19 73.75 74.73 0.5890E+01 0.8584E+01 0.5885E+01 0.4828E+01 23 9.97 82.86 85.55 83.38 82.58 0.4339E+01 0.8584E+01 0.4842E+01 0.3995E+01 25 11.65 90.24 100.00 90.62 88.78 0.4436E+01 0.8584E+01 0.3764E+01 0.3397E+01 27 13.16 95.81 112.98 95.61 93.59 0.3086E+01 0.8584E+01 0.2853E+01 0.2970E+01 29 14.70 100.12 126.21 99.88 97.88 0.2452E+01 0.8584E+01 0.2780E+01 0.2614E+01 31 16.24 103.56 139.41 103.66 101.67 0.2060E+01 0.8584E+01 0.2160E+01 0.2321E+01 33 17.98 106.60 154.31 106.94 105.45 0.1466E+01 0.8584E+01 0.1650E+01 0.2046E+01 35 19.77 109.33 169.67 109.55 108.90 0.1584E+01 0.8584E+01 0.1294E+01 0.1812E+01 37 21.54 112.15 184.95 111.63 111.94 0.1584E+01 0.8584E+01 0.1066E+01 0.1617E+01 ----------------------------------------------------------------------------------------------------------------------------





A.1 – 26


: :


1) 2)

1.7500" 2.5625" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.3125" cl = 1.2500" nc = 1 X 4

------------------------------



lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters

S.L.Lipson (1968) B3-4


Tested by Test Id.


I - 14

0

20

40

60

80

100

120

140

160

180

200

0

6

ta

column

18

beam

pc pc pc pc qc

gc

24

30

36

42

48

54




12

gb

60

A.1 – 27


Moment ( kip-inch )

R t A3 P3


Q3 =



-0.17436531E+04

-13



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.40829917E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.94259256E+02 -0.95165788E+03 0.37669182E+04 -0.71368433E+04 0.60801595E+04 Rj0 = 16.4700 RKj = 0.12200905E+01



A.1 – 28


: :


1) 2)

1.7500" 1.9375" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.3125" cl = 1.2500" nc = 1 X 4

------------------------------



lu = gc = pc =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"


Major parameters

S.L.Lipson (1968) C-4


Tested by Test Id.


I - 15

0

20

40

60

80

100

120

140

160

180

200

0

3

ta

column

9

beam

pc pc pc pc qc

gc

12

15

18

21

24

27




6

gb

30

A.1 – 29


Moment ( kip-inch )

R t A3 P3


Q3 =



0.24686708E+04

-13



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.14809083E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.63363439E+02 0.13333942E+03 -0.20505799E+04 0.52958687E+04 -0.57682947E+04 Rj0 = 1.9100 3.3200 4.9100 9.8700 RKj = -0.91381997E+01 0.82933853E+01 0.35128252E+01 0.13386231E+00



A.1 – 30


: :


1) 2)

1.7500" 1.9375" 3.0000"

ll = 1.7500" cu = 1.2500" nb = 1 X 4

ta = 0.3125" cl = 1.2500" nc = 1 X 4

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 125.71 8.73 27 128.72 9.22 28 131.74 9.72 29 133.76 10.22 30 135.79 10.73 31 137.82 11.23 32 139.84 11.73 33 141.57 12.29 34 143.29 12.85 35 145.02 13.41


lu = gc = pc =


Remark

lp = 11.5000" gb = 3.2500" pb = 3.0000"


Major parameters

S.L.Lipson (1968) D-4


Tested by Test Id.


I - 16

0

20

40

60

80

100

120

140

160

180

200

0

3

ta

column

9

beam

pc pc pc pc qc

gc

12

15

18

21

24

27




6

gb

30

A.1 – 31


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-6

Q3 =



0.54198283E+04

-13






A.1 – 32


: :


1) 2)

7.7500" 1.2500"

ll = cl =

7.7500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------


Connection plate welded to 1" mounting plate.

lu = cu =


Remark

lp = 5.5000" gb = 2.5000" nb = 1 X 2

Canada Fasteners: A325- -3/4"D 15/16" Oversize holes Material : A36 Fy = 48.75 ksi Fu = 71.76 ksi

Major parameters

S.L.Lipson (1968) P1-2/1

Column : -Beam : W21X62 Angle : --

Tested by Test Id.

Connection type : Single web-angle connections Mode : Bolted-to-beam and welded-to-column

I - 17

0

10

20

30

40

50

60

70

80

90

100

0


5

15

20

25

30

qc

35

pc pc pc pc


10

Material : A36 Fy = 48.75 ksi : Experimental : M. Exponential

ta

column

40

gc

45

50

A.1 – 33


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1503E+02 0.1465E+02 3 0.28 4.26 4.37 0.1503E+02 0.1559E+02 5 0.57 8.52 8.62 0.1502E+02 0.1416E+02 7 0.85 12.78 12.34 0.1275E+02 0.1203E+02 9 1.34 17.09 17.34 0.8859E+01 0.8683E+01 11 1.82 21.40 20.98 0.7194E+01 0.6469E+01 13 2.55 24.83 25.02 0.4686E+01 0.4848E+01 15 3.43 28.78 28.91 0.4357E+01 0.4102E+01 17 4.43 32.69 32.69 0.3506E+01 0.3508E+01 19 5.38 36.04 35.72 0.2999E+01 0.2828E+01 21 7.08 39.61 39.45 0.1564E+01 0.1584E+01 23 9.52 41.55 41.72 0.5141E+00 0.4274E+00 25 11.99 42.11 42.13 0.2250E+00 -0.7261E-02 27 14.63 42.16 41.95 -0.1658E+00 -0.9566E-01 29 17.42 41.70 41.70 -0.9162E-01 -0.7384E-01 31 19.71 41.63 41.56 -0.3054E-01 -0.4663E-01 33 22.01 41.56 41.48 0.2206E+00 -0.2677E-01 35 24.51 42.79 43.49 0.1153E+01 0.1352E+01 37 26.27 45.65 45.88 0.1654E+01 0.1357E+01 39 28.31 49.10 48.65 0.1696E+01 0.1361E+01 ------------------------------------------------------------------------------



A.1 – 34

-0.10066890E+03



: :


1) 2)

7.7500" 1.2500"

ll = cl =

7.7500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 5.5000" gb = 2.5000" nb = 1 X 2


Major parameters

S.L.Lipson (1968) P1-2/2


Tested by Test Id.


I - 18

0

10

20

30

40

50

60

70

80

90

100

0


9

27

36

45

54

qc

63

pc pc pc pc


18


ta

column

72

gc

81

90

A.1 – 35


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1327E+02 0.1498E+02 3 0.28 3.75 4.01 0.1327E+02 0.1344E+02 5 0.56 7.50 7.61 0.1327E+02 0.1208E+02 7 0.90 11.37 11.40 0.1037E+02 0.1067E+02 9 1.28 15.35 15.22 0.1037E+02 0.9282E+01 11 1.75 19.31 19.23 0.7105E+01 0.7860E+01 13 2.30 23.24 23.18 0.6340E+01 0.6493E+01 15 2.96 26.78 26.98 0.5437E+01 0.5212E+01 17 3.61 30.33 30.04 0.4676E+01 0.4206E+01 19 5.04 34.63 34.86 0.2762E+01 0.2659E+01 21 6.74 38.83 38.34 0.2034E+01 0.1542E+01 23 10.99 41.42 41.70 0.2764E+00 0.2670E+00 25 15.59 41.59 41.71 -0.1736E+00 -0.1698E+00 27 20.49 40.74 40.70 -0.1727E+00 -0.2228E+00 29 25.33 39.91 39.71 -0.1718E+00 -0.1785E+00 31 30.52 38.84 38.97 -0.2364E+00 -0.1061E+00 33 36.04 38.56 38.56 0.2876E-01 -0.4521E-01 35 40.47 40.17 40.05 0.8175E+00 0.7277E+00 37 44.75 43.67 43.21 0.5542E+00 0.7471E+00 39 48.93 44.91 45.47 0.2969E+00 -0.1947E+00 41 53.65 44.81 44.57 -0.2736E+00 -0.1873E+00 43 58.90 43.38 43.60 -0.2737E+00 -0.1830E+00 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.52609583E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.67468569E+00 0.90064598E+01 0.11974384E+03 -0.50358102E+03 0.83982281E+03 Rj0 = 16.8200 38.3000 48.0000 RKj = 0.33234553E-01 0.74106593E+00 -0.95332683E+00


A.1 – 36

-0.42836885E+03



: :


1) 2)

6.2500" 1.2500"

ll = cl =

6.2500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 131.53 13.61 27 133.45 14.78 28 135.36 15.95 29 137.27 17.13 30 140.09 18.33 31 142.91 19.53 32 145.73 20.72 33 148.32 21.92 34 150.91 23.12 35 153.50 24.32 36 155.87 25.49 37 158.24 26.67 38 160.61 27.84 39 162.71 29.15 40 164.81 30.46 41 166.90 31.77


lu = cu =


Remark

lp = 8.5000" gb = 2.5000" nb = 1 X 3


Major parameters

S.L.Lipson (1968) P1-3/1


Tested by Test Id.


I - 19

0

25

50

75

100

125

150

175

200

225

250

0

5

ta

column

15

beam

pc pc pc pc qc

gc

20

25

30

35

40




10

gb

45

50

A.1 – 37


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.5821E+02 0.6755E+02 3 0.23 13.38 14.03 0.5821E+02 0.5522E+02 5 0.46 26.76 25.62 0.5821E+02 0.4610E+02 7 0.83 40.22 40.71 0.2642E+02 0.3584E+02 9 1.31 54.14 55.76 0.3184E+02 0.2742E+02 11 1.75 66.35 66.67 0.2332E+02 0.2231E+02 13 2.22 77.18 76.20 0.2269E+02 0.1834E+02 15 2.86 87.27 86.55 0.1130E+02 0.1433E+02 17 4.08 99.58 100.50 0.8339E+01 0.8989E+01 19 5.32 108.79 109.27 0.6240E+01 0.5389E+01 21 7.44 117.72 116.54 0.3613E+01 0.1933E+01 23 10.02 125.13 124.34 0.2306E+01 0.2367E+01 25 12.41 129.40 129.40 0.1783E+01 0.1954E+01 27 14.78 133.45 133.93 0.1630E+01 0.1898E+01 29 17.13 137.27 138.42 0.1987E+01 0.1935E+01 31 19.53 142.91 143.12 0.2352E+01 0.1982E+01 33 21.92 148.32 147.91 0.2163E+01 0.2016E+01 35 24.32 153.50 152.77 0.2089E+01 0.2037E+01 37 26.67 158.24 157.57 0.2017E+01 0.2050E+01 39 29.15 162.71 162.67 0.1603E+01 0.2057E+01 41 31.77 166.90 168.06 0.1603E+01 0.2060E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.29347000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.14223767E+02 0.65462457E+02 -0.31896045E+03 0.47501272E+03 -0.26606636E+01 Rj0 = 7.4400 RKj = 0.20641279E+01


A.1 – 38

-0.11524991E+03



: :


1) 2)

6.2500" 1.2500"

ll = cl =

6.2500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 8.5000" gb = 2.5000" nb = 1 X 3


Major parameters

S.L.Lipson (1968) P1-3/2


Tested by Test Id.


I - 20

0

20

40

60

80

100

120

140

160

180

200

0

9

ta

column

27

beam

pc pc pc pc qc

gc

36

45

54

63

72




18

gb

81

90

A.1 – 39


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.4658E+02 0.6148E+02 3 0.31 14.65 16.08 0.4658E+02 0.4197E+02 5 0.63 29.31 27.06 0.3625E+02 0.2870E+02 7 1.24 39.18 39.57 0.1607E+02 0.1395E+02 9 2.11 50.11 50.96 0.1076E+02 0.1200E+02 11 3.36 63.44 63.13 0.8869E+01 0.8123E+01 13 4.40 71.34 70.68 0.6894E+01 0.6554E+01 15 6.30 77.59 78.02 0.4405E+00 0.7680E+00 17 11.40 78.44 78.10 0.1653E+00 0.6244E-02 19 16.49 79.28 79.34 0.1653E+00 0.3426E+00 21 21.69 80.68 80.82 0.3703E+00 0.2403E+00 23 27.00 82.65 82.54 0.5250E+00 0.4844E+00 25 32.47 86.39 86.67 0.1106E+01 0.1050E+01 27 37.41 93.73 93.50 0.1631E+01 0.1798E+01 29 42.01 101.87 102.69 0.2137E+01 0.2172E+01 31 45.74 110.97 111.22 0.2529E+01 0.2389E+01 33 49.48 120.75 120.45 0.2657E+01 0.2540E+01 35 54.91 135.49 134.65 0.2433E+01 0.2674E+01 37 59.80 147.65 147.90 0.2937E+01 0.2740E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.53766583E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.18854298E+03 -0.17557310E+04 0.88496166E+04 -0.20536968E+05 0.22039214E+05 Rj0 = 1.5500 5.4900 36.0000 RKj = 0.64030424E+01 -0.38209022E+01 0.23020071E+00


A.1 – 40

-0.88082437E+04



: :


1) 2)

4.7500" 1.2500"

ll = cl =

4.7500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 186.09 21.06 27 197.30 22.48 28 205.84 23.65 29 214.38 24.82 30 221.76 26.06 31 229.14 27.30 32 236.51 28.54 33 241.58 29.83 34 246.65 31.13 35 251.72 32.43 36 256.50 33.91 37 261.28 35.38 38 266.06 36.86


lu = cu =


Remark

lp = 11.5000" gb = 2.5000" nb = 1 X 4


Major parameters

S.L.Lipson (1968) P1-4/1


Tested by Test Id.


I - 21

0

35

70

105

140

175

210

245

280

315

350

0

6

ta

column

18

beam

pc pc pc pc qc

gc

24

30

36

42

48




12

gb

54

60

A.1 – 41


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.6209E+02 0.5979E+02 3 0.37 22.96 23.54 0.6210E+02 0.6428E+02 5 0.74 45.92 46.02 0.6210E+02 0.5622E+02 7 1.12 65.58 65.14 0.4203E+02 0.4444E+02 9 1.54 80.55 81.13 0.3034E+02 0.3232E+02 11 2.41 99.50 101.19 0.1781E+02 0.1583E+02 13 4.08 118.18 117.21 0.6056E+01 0.6013E+01 15 6.81 126.21 127.17 0.1920E+01 0.1567E+01 17 9.41 131.31 131.35 0.1993E+01 0.1970E+01 19 12.17 136.81 136.83 0.2490E+01 0.2330E+01 21 14.69 144.22 144.11 0.3851E+01 0.3444E+01 23 17.36 157.08 158.67 0.6423E+01 0.7298E+01 25 19.64 174.88 175.59 0.7845E+01 0.7464E+01 27 22.48 197.30 196.55 0.7563E+01 0.7269E+01 29 24.82 214.38 213.28 0.6638E+01 0.6972E+01 31 27.30 229.14 230.13 0.5962E+01 0.6655E+01 33 29.83 241.58 241.79 0.3906E+01 0.3737E+01 35 32.43 251.72 251.20 0.3593E+01 0.3530E+01 37 35.38 261.28 261.37 0.3237E+01 0.3372E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.35337667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.21038004E+03 0.27259985E+04 -0.12308029E+05 0.26201795E+05 -0.25438158E+05 Rj0 = 8.0300 16.0000 28.0000 RKj = 0.27054835E+01 0.30864531E+01 -0.26459694E+01


A.1 – 42

0.91769926E+04



: :


1) 2)

4.7500" 1.2500"

ll = cl =

4.7500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 11.5000" gb = 2.5000" nb = 1 X 4


Major parameters

S.L.Lipson (1968) P1-4/2


Tested by Test Id.


I - 22

0

35

70

105

140

175

210

245

280

315

350

0

6

ta

column

18

beam

pc pc pc pc qc

gc

24

30

36

42

48




12

gb

54

60

A.1 – 43


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 44

0.59909372E+04



: :


1) 2)

3.2500" 1.2500"

ll = cl =

3.2500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 14.5000" gb = 2.5000" nb = 1 X 5


Major parameters

S.L.Lipson (1968) P1-5/1


Tested by Test Id.


I - 23

0

55

110

165

220

275

330

385

440

495

550

0

5

ta

column

15

beam

pc pc pc pc qc

gc

20

25

30

35

40




10

gb

45

50

A.1 – 45


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 46

0.16960721E+05



: :


1) 2)

3.2500" 1.2500"

ll = cl =

3.2500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 14.5000" gb = 2.5000" nb = 1 X 5


Major parameters

S.L.Lipson (1968) P1-5/2


Tested by Test Id.


I - 24

0

55

110

165

220

275

330

385

440

495

550

0

6

ta

column

18

beam

pc pc pc pc qc

gc

24

30

36

42

48




12

gb

54

60

A.1 – 47


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1609E+03 0.2200E+03 3 0.27 44.22 49.58 0.1609E+03 0.1466E+03 5 0.55 88.43 83.14 0.1263E+03 0.1013E+03 7 1.01 119.88 119.20 0.6857E+02 0.6149E+02 9 1.74 152.61 154.30 0.3385E+02 0.3915E+02 11 2.75 186.63 188.09 0.3107E+02 0.2919E+02 13 3.78 215.83 213.84 0.2455E+02 0.2041E+02 15 6.01 239.82 238.56 0.2853E+01 0.3059E+01 17 8.99 240.89 242.62 0.7231E+00 -0.1081E+01 19 11.60 242.78 241.32 0.1126E+01 0.6145E+00 21 15.32 249.10 250.63 0.2800E+01 0.2266E+01 23 18.39 260.46 259.67 0.5192E+01 0.3379E+01 25 21.98 290.87 292.99 0.9701E+01 0.1454E+02 27 23.67 314.35 317.38 0.2221E+02 0.1432E+02 29 25.24 341.31 339.62 0.1342E+02 0.1409E+02 31 28.59 381.42 386.10 0.1095E+02 0.7326E+01 33 31.86 414.00 409.48 0.8583E+01 0.7012E+01 35 34.20 431.77 425.73 0.6739E+01 0.6862E+01 37 37.06 442.85 445.17 0.1258E+01 0.6742E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.35222917E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.24588172E+03 0.12527586E+03 -0.66192245E+04 0.21115721E+05 -0.23645436E+05 Rj0 = 6.0100 15.3200 20.1100 28.5900 RKj = 0.34947968E+01 -0.18202207E+01 0.11214554E+02 -0.63126248E+01


A.1 – 48

0.90181708E+04



: :


1) 2)

1.7500" 1.2500"

ll = cl =

1.7500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 17.5000" gb = 2.5000" nb = 1 X 6


Major parameters

S.L.Lipson (1968) P1-6/1


Tested by Test Id.


I - 25

0

85

170

255

340

425

510

595

680

765

850

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 49


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2302E+03 0.2635E+03 3 0.29 66.15 69.84 0.2301E+03 0.2231E+03 5 0.57 132.31 128.72 0.2301E+03 0.1873E+03 7 0.93 187.77 187.93 0.1072E+03 0.1496E+03 9 1.35 232.55 242.51 0.1366E+03 0.1131E+03 11 1.66 283.31 274.90 0.1244E+03 0.9052E+02 13 2.29 318.88 320.20 0.6190E+02 0.5760E+02 15 3.26 360.55 359.96 0.2609E+02 0.2785E+02 17 4.66 382.89 385.38 0.1163E+02 0.1212E+02 19 6.59 403.37 403.62 0.1014E+02 0.8127E+01 21 8.62 423.15 421.76 0.9451E+01 0.9493E+01 23 10.48 440.56 439.11 0.9216E+01 0.8863E+01 25 11.97 456.69 451.21 0.1307E+02 0.7328E+01 27 13.81 484.41 490.32 0.1599E+02 0.2027E+02 29 15.72 521.74 526.77 0.2223E+02 0.1808E+02 31 17.80 564.17 562.46 0.1825E+02 0.1625E+02 33 19.59 594.66 590.48 0.1558E+02 0.1516E+02 35 21.28 618.41 615.36 0.1278E+02 0.1446E+02 37 23.03 640.89 640.33 0.1219E+02 0.1398E+02 39 25.52 669.14 674.59 0.1135E+02 0.1358E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.24862000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.24043658E+01 0.10695429E+03 -0.28743541E+04 0.14516606E+05 -0.21549396E+05 Rj0 = 5.7600 12.0000 RKj = -0.20585343E+01 0.15255662E+02


A.1 – 50

0.10312831E+05



: :


1) 2)

1.7500" 1.2500"

ll = cl =

1.7500" 1.2500"

ta = pb =

0.2500" 3.0000"

------------------------------



lu = cu =


Remark

lp = 17.5000" gb = 2.5000" nb = 1 X 6


Major parameters

S.L.Lipson (1968) P1-6/2


Tested by Test Id.


I - 26

0

85

170

255

340

425

510

595

680

765

850

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 51


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 52

0.51997757E+05



: :


1) 2)

8.1250" 1.2500"

ll = cl =

8.1250" 1.2500"

ta = pb =

0.3125" 2.2500"


1/4" fillet weld at heel of angle. Connection rotated under constant shear.

lu = cu =


Remark

lp = 4.7500" gb = 2.5000" nb = 1 X 2


Major parameters

S.L.Lipson (1968) G-2/1


Tested by Test Id.


I - 27

0

10

20

30

40

50

60

70

80

90

100

0


5

15

20

25

30

qc

35

pc pc pc pc


10


ta

column

40

gc

45

50

A.1 – 53


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1835E+02 0.1730E+02 3 0.25 4.51 4.36 0.1835E+02 0.1831E+02 5 0.49 9.03 9.03 0.1835E+02 0.1962E+02 7 0.74 13.54 13.97 0.2113E+02 0.2047E+02 9 0.91 17.48 17.49 0.2307E+02 0.2067E+02 11 1.08 21.42 21.02 0.2307E+02 0.2055E+02 13 1.29 25.50 25.24 0.1724E+02 0.2004E+02 15 1.53 29.73 30.05 0.1723E+02 0.1907E+02 17 1.76 33.79 34.27 0.1846E+02 0.1795E+02 19 1.97 37.68 37.94 0.1846E+02 0.1684E+02 21 2.18 41.83 41.39 0.2077E+02 0.1573E+02 23 2.46 45.88 45.57 0.1070E+02 0.1437E+02 25 3.95 48.77 49.22 0.3972E+00 -0.1327E+00 27 5.90 48.97 48.73 -0.8392E-01 -0.1860E+00 29 7.60 46.48 47.41 -0.2162E+01 -0.1269E+01 31 10.09 44.49 44.79 0.3026E+01 -0.4565E+00 33 10.73 47.07 46.60 0.3469E+01 0.2363E+01 35 12.67 49.16 49.54 0.3744E+00 0.9508E+00 37 14.40 49.58 49.84 0.1278E+00 -0.4868E+00 39 16.74 47.62 47.11 -0.7730E+00 0.4476E+00 41 18.99 47.06 47.60 -0.9157E-01 0.5973E-01 43 21.85 47.37 47.56 0.2033E+00 -0.4540E-01 45 24.41 48.11 47.48 0.1267E-01 -0.1576E-01 47 26.86 47.49 47.50 -0.1237E+00 0.3053E-01 49 28.85 47.45 47.59 -0.2082E-01 0.6236E-01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.27947750E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.45989844E+02 -0.11508069E+04 0.63338620E+04 -0.13397834E+05 0.11790868E+05 Rj0 = 2.6300 5.9000 6.7700 9.0100 10.0900 11.8400 15.3100 16.7400 RKj = -0.10789485E+02 -0.37200075E+00 0.25173867E+00 0.42904666E+01 0.37731939E+01 0.10007323E+01 -0.14713868E+00 0.21218320E+01


A.1 – 54

-0.34855290E+04



: :


1) 2)

6.5000" 1.7500"

ll = cl =

6.5000" 1.7500"

ta = pb =

0.3125" 2.2500"

------------------------------



lu = cu =


Remark

lp = 8.0000" gb = 2.5000" nb = 1 X 3


Major parameters

S.L.Lipson (1968) G-3/1


Tested by Test Id.


I - 28

0

15

30

45

60

75

90

105

120

135

150

0

5

ta

column

15

beam

pc pc pc pc qc

gc

20

25

30

35

40




10

gb

45

50

A.1 – 55


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.3606E+02 0.4050E+02 3 0.28 10.20 10.84 0.3606E+02 0.3642E+02 5 0.57 20.41 20.74 0.3606E+02 0.3365E+02 7 0.85 30.61 29.93 0.3336E+02 0.3137E+02 9 1.21 41.48 40.82 0.2992E+02 0.2855E+02 11 1.61 51.54 51.47 0.2168E+02 0.2533E+02 13 2.03 60.80 61.50 0.2051E+02 0.2167E+02 15 2.53 70.26 71.16 0.1913E+02 0.1742E+02 17 3.07 79.03 79.42 0.1362E+02 0.1304E+02 19 3.72 87.77 86.34 0.1084E+02 0.8560E+01 21 4.67 92.67 92.01 0.1909E+01 0.3660E+01 23 6.48 93.60 94.79 0.6877E+00 -0.1690E+00 25 8.82 93.36 93.14 -0.7987E+00 -0.7186E+00 27 11.53 92.85 92.50 0.3349E+00 0.2669E+00 29 14.30 94.73 94.57 0.1067E+01 0.1221E+01 31 16.72 97.56 97.71 0.1286E+01 0.1332E+01 33 19.07 101.08 100.79 0.1692E+01 0.1267E+01 35 21.37 103.59 103.58 0.3959E+00 0.1162E+01 37 23.46 105.13 105.92 0.1080E+01 0.1075E+01 39 25.61 108.19 108.15 0.1744E+01 0.1006E+01 41 27.77 113.99 113.50 0.3691E+01 0.4061E+01 43 29.86 121.69 121.93 0.3692E+01 0.4031E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.28418250E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.12700454E+02 0.56826575E+02 -0.15822150E+04 0.51810900E+04 -0.57035544E+04 Rj0 = 4.7600 13.3000 26.7300 RKj = 0.52764118E+00 0.35236740E+00 0.31026779E+01


A.1 – 56

0.21284967E+04



: :


1) 2)

4.8750" 2.2500"

ll = cl =

4.8750" 2.2500"

ta = pb =

0.3125" 2.2500"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 136.98 11.58 27 138.15 12.35 28 139.13 13.26 29 140.10 14.18 30 140.31 15.41 31 140.52 16.64 32 142.31 17.68 33 143.99 18.50 34 145.68 19.31 35 149.35 20.38 36 153.03 21.45 37 157.75 22.45 38 162.47 23.46 39 169.53 24.68 40 176.60 25.91 41 181.98 27.00 42 187.36 28.10 43 192.78 29.07 44 198.19 30.04


lu = cu =


Remark

lp = 12.0000" gb = 2.5000" nb = 1 X 4


Major parameters

S.L.Lipson (1968) G-4/1


Tested by Test Id.


I - 29

0

25

50

75

100

125

150

175

200

225

250

0

5

ta

column

15

beam

pc pc pc pc qc

gc

20

25

30

35

40




10

gb

45

50

A.1 – 57


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.7632E+02 0.8798E+02 3 0.23 17.63 19.33 0.7636E+02 0.7924E+02 5 0.46 35.26 36.59 0.7632E+02 0.7029E+02 7 0.68 52.28 51.10 0.7894E+02 0.6204E+02 9 0.95 67.41 66.37 0.4262E+02 0.5273E+02 11 1.27 81.27 81.84 0.4651E+02 0.4266E+02 13 1.54 94.57 92.28 0.4155E+02 0.3550E+02 15 2.25 108.79 111.94 0.2062E+02 0.2109E+02 17 3.34 127.72 127.22 0.1113E+02 0.8517E+01 19 4.60 135.63 133.38 0.1894E+01 0.2216E+01 21 6.72 133.73 134.20 -0.3357E+00 -0.5689E+00 23 8.67 133.59 135.08 0.4595E+00 0.4291E+00 25 10.80 135.80 136.20 0.1314E+01 0.6292E+00 27 12.35 138.15 137.29 0.1309E+01 0.7700E+00 29 14.18 140.10 138.81 0.6847E+00 0.8940E+00 31 16.64 140.52 141.16 0.1002E+01 0.1005E+01 33 18.50 143.99 143.08 0.2072E+01 0.1060E+01 35 20.38 149.35 149.17 0.3437E+01 0.4903E+01 37 22.45 157.75 159.37 0.4698E+01 0.4931E+01 39 24.68 169.53 170.41 0.5747E+01 0.4951E+01 41 27.00 181.98 181.91 0.4938E+01 0.4963E+01 43 29.07 192.78 192.16 0.5566E+01 0.4969E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.27921167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.10082154E+02 -0.52516263E+02 0.58976630E+03 -0.84857185E+03 0.77994126E+03 Rj0 = 6.7200 19.3100 RKj = 0.11742254E+01 0.38042031E+01


A.1 – 58

-0.32977486E+03



: :


1) 2)

3.2500" 2.7500"

ll = cl =

3.2500" 2.7500"

ta = pb =

0.3125" 2.2500"

------------------------------



lu = cu =


Remark

lp = 14.5000" gb = 2.5000" nb = 1 X 5


Major parameters

S.L.Lipson (1968) G-5/1


Tested by Test Id.


I - 30

0

40

80

120

160

200

240

280

320

360

400

0

5

ta

column

15

beam

pc pc pc pc qc

gc

20

25

30

35

40




10

gb

45

50

A.1 – 59


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 60

0.60904488E+04




: :

1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

------------------------------

ta

column

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------51 259.82 23.76

0.3750" 3.0000"


1/4" fillet weld at heel, top and bottom of angle. Connection subject to moment and shear.

lu = cu =


Remark

lp = 14.5000" gb = 2.5000" nb = 1 X 5

Canada Fasteners: A325- -3/4"D 13/16" Oversize holes Material : G40.21 Fy = 55.40 ksi Fu = 77.80 ksi

Major parameters

S.L.Lipson (1977) A1-5

Column : T=44",TW=5/8" Beam : -Angle : 4 X 3 X 3/8

Tested by Test Id.

I - 31

Moment ( kip-inch )


0

35

70

105

140

175

210

245

280

315

350

0

gb

4

12

pc pc pc pc qc

gc

16

20

24

28

32

Material : G40.21 Fy = 55.40 ksi : Experimental : M. Exponential

beam


8


36

40

A.1 – 61


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1126E+03 0.1089E+03 3 0.23 25.79 26.27 0.1126E+03 0.1156E+03 5 0.46 51.57 51.55 0.1126E+03 0.1037E+03 7 0.70 74.51 74.65 0.7798E+02 0.8600E+02 9 0.96 94.61 94.53 0.7798E+02 0.6889E+02 11 1.30 114.10 115.02 0.4422E+02 0.5191E+02 13 1.73 132.99 134.01 0.4174E+02 0.3803E+02 15 2.22 151.98 149.73 0.3054E+02 0.2672E+02 17 3.01 165.49 164.36 0.1064E+02 0.1002E+02 19 4.58 159.22 157.30 -0.1679E+02 -0.1616E+02 21 5.54 136.76 138.56 -0.2147E+02 -0.2156E+02 23 6.49 118.30 118.54 -0.1950E+02 -0.1982E+02 25 7.64 102.73 99.49 -0.9363E+01 -0.1279E+02 27 9.13 88.77 88.11 -0.9322E+01 -0.2761E+01 29 10.72 88.57 89.91 0.9653E+01 0.4282E+01 31 12.16 107.75 105.98 0.1746E+02 0.1816E+02 33 13.27 130.38 130.73 0.2473E+02 0.2807E+02 35 14.15 152.08 155.26 0.2704E+02 0.2776E+02 37 15.03 177.82 179.33 0.2934E+02 0.2712E+02 39 15.82 201.89 200.69 0.3121E+02 0.2641E+02 41 16.54 224.32 219.42 0.3121E+02 0.2573E+02 43 17.59 245.83 245.91 0.1492E+02 0.2476E+02 45 19.22 263.83 267.09 0.8232E+01 0.4288E+01 47 20.86 269.78 269.04 -0.2489E+01 -0.2737E+01 49 22.25 264.69 264.82 -0.4911E+01 -0.3329E+01 51 23.76 259.82 259.44 -0.1856E+01 -0.3778E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.22658500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.28671862E+03 0.56504464E+04 -0.33184380E+05 0.78892620E+05 -0.79907960E+05 Rj0 = 11.4800 12.8300 18.2800 20.1600 RKj = 0.11136377E+02 0.94927919E+01 -0.19178599E+02 -0.60417455E+01


A.1 – 62

0.28984325E+05



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 476.04 7.75 27 469.92 8.55 28 463.79 9.36 29 472.52 10.02 30 481.24 10.67 31 491.81 11.52 32 502.38 12.36 33 507.04 13.28 34 511.70 14.21 35 507.19 15.07 36 502.69 15.93 37 510.32 16.82 38 517.94 17.71 39 541.00 18.78 40 563.46 19.52 41 585.91 20.25 42 594.56 20.86 43 603.20 21.48 44 595.24 22.09 45 587.27 22.71


lu = cu =


Remark

lp = 17.5000" gb = 2.5000" nb = 1 X 6


Major parameters



Tested by Test Id.


I - 32

0

75

150

225

300

375

450

525

600

675

750

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 63


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2928E+03 0.3023E+03 3 0.18 51.24 53.09 0.2926E+03 0.2994E+03 5 0.35 102.48 103.74 0.2926E+03 0.2775E+03 7 0.53 153.72 149.90 0.2928E+03 0.2495E+03 9 0.78 207.84 208.69 0.1686E+03 0.2099E+03 11 1.12 264.83 272.36 0.1771E+03 0.1691E+03 13 1.42 319.74 318.68 0.1846E+03 0.1437E+03 15 1.80 371.78 368.50 0.1063E+03 0.1197E+03 17 2.26 420.94 418.28 0.9315E+02 0.9598E+02 19 3.05 476.73 479.01 0.5634E+02 0.5822E+02 21 3.78 508.24 509.78 0.3690E+02 0.2680E+02 23 5.59 517.51 512.24 -0.1982E+02 -0.1477E+02 25 7.17 482.55 485.55 -0.1112E+02 -0.1577E+02 27 8.55 469.92 469.00 -0.7652E+01 -0.7762E+01 29 10.02 472.52 470.67 0.1323E+02 0.1065E+02 31 11.52 491.81 490.29 0.1252E+02 0.1486E+02 33 13.28 507.04 505.80 0.5059E+01 0.2830E+01 35 15.07 507.19 510.35 -0.5229E+01 0.2089E+01 37 16.82 510.32 512.93 0.8566E+01 0.8429E+00 39 18.78 541.00 541.34 0.2690E+02 0.2573E+02 41 20.25 585.91 578.57 0.2160E+02 0.2505E+02 43 21.48 603.20 609.04 0.6230E+00 0.2463E+02 45 22.71 587.27 586.07 -0.1292E+02 -0.1885E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21113083E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.37456435E+03 0.70517529E+04 -0.38287138E+05 0.84392080E+05 -0.79384219E+05 Rj0 = 9.3600 12.3600 17.7100 21.4800 RKj = 0.10843076E+02 -0.13271110E+02 0.26121797E+02 -0.43187906E+02


A.1 – 64

0.27105178E+05



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"

------------------------------



lu = cu =


Remark

lp = 20.5000" gb = 2.5000" nb = 1 X 7


Major parameters



Tested by Test Id.


I - 33

0

150

300

450

600

750

900

1050

1200

1350

1500

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 65


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.4601E+03 0.5767E+03 3 0.20 91.01 98.40 0.4601E+03 0.4322E+03 5 0.40 182.01 175.10 0.3957E+03 0.3509E+03 7 0.78 285.44 292.08 0.3656E+03 0.2755E+03 9 0.95 355.25 337.46 0.3338E+03 0.2554E+03 11 1.30 419.37 422.25 0.1802E+03 0.2201E+03 13 1.72 494.67 505.47 0.1808E+03 0.1793E+03 15 2.17 573.55 575.50 0.1730E+03 0.1346E+03 17 2.89 654.97 648.56 0.6627E+02 0.7012E+02 19 3.96 690.22 687.61 0.5968E+01 0.1032E+02 21 5.41 676.32 680.03 -0.5473E+01 -0.1257E+02 23 6.81 666.87 665.33 -0.7727E+01 -0.6358E+01 25 8.42 665.34 664.68 0.5584E+01 0.5025E+01 27 10.15 688.24 686.26 0.1993E+02 0.1822E+02 29 12.02 720.46 721.44 0.1457E+02 0.1857E+02 31 13.74 738.79 732.97 0.5806E+01 -0.7805E+01 33 15.34 762.94 762.41 0.2378E+02 0.4262E+02 35 17.01 818.94 831.51 0.4325E+02 0.4036E+02 37 18.56 889.83 893.04 0.4823E+02 0.3879E+02 39 20.00 955.97 947.90 0.4399E+02 0.3777E+02 41 21.77 1016.70 1014.12 0.2761E+02 0.3695E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21496417E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.33266444E+03 0.93120855E+02 -0.15974874E+05 0.56707555E+05 -0.67493208E+05 Rj0 = 9.2300 12.9700 14.5100 RKj = 0.69192410E+01 -0.24058586E+02 0.52968014E+02


A.1 – 66

0.27092526E+05



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"

------------------------------



lu = cu =


Remark

lp = 23.5000" gb = 2.5000" nb = 1 X 8


Major parameters



Tested by Test Id.


I - 34

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 67


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.6099E+03 0.6200E+03 3 0.20 119.91 122.67 0.6099E+03 0.6138E+03 5 0.39 239.81 237.86 0.6099E+03 0.5531E+03 7 0.63 358.39 359.61 0.4141E+03 0.4618E+03 9 0.92 475.65 476.42 0.3715E+03 0.3670E+03 11 1.24 580.93 582.59 0.3223E+03 0.2889E+03 13 1.65 686.36 687.34 0.2153E+03 0.2296E+03 15 2.14 791.96 788.96 0.1968E+03 0.1882E+03 17 2.88 917.17 911.25 0.1376E+03 0.1422E+03 19 3.73 1003.34 1009.71 0.9503E+02 0.9189E+02 21 5.58 1103.59 1097.09 0.6023E+01 0.1306E+02 23 6.72 1093.76 1100.13 -0.1914E+02 -0.4483E+01 25 7.86 1059.81 1053.99 -0.3829E+02 -0.4115E+02 27 8.98 1007.69 1009.34 -0.4382E+02 -0.3838E+02 29 10.75 976.49 973.15 0.7547E+01 0.4825E-01 31 12.29 1018.77 1020.52 0.4954E+02 0.6397E+02 33 14.05 1120.34 1133.94 0.7249E+02 0.6453E+02 35 15.69 1250.33 1238.83 0.7089E+02 0.6391E+02 37 17.17 1343.81 1333.19 0.5624E+02 0.6308E+02 39 19.09 1435.12 1453.12 0.2454E+02 0.6212E+02 41 20.38 1446.72 1434.77 -0.1011E+01 -0.1456E+02 43 22.14 1395.88 1408.67 -0.4324E+02 -0.1503E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20905667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.77242177E+03 0.11402540E+05 -0.50995818E+05 0.98826485E+05 -0.84588218E+05 Rj0 = 6.7200 9.9400 11.5600 19.0900 RKj = -0.33559306E+02 0.32743618E+02 0.61284992E+02 -0.76186241E+02


A.1 – 68

0.27240109E+05



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"



lu = cu =


Remark

lp = 26.5000" gb = 2.5000" nb = 1 X 9


Major parameters



Tested by Test Id.


I - 35

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 69


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.8624E+03 0.1019E+04 3 0.24 209.05 196.12 0.7245E+03 0.6470E+03 5 0.67 415.38 414.01 0.4351E+03 0.4283E+03 7 1.07 573.28 577.82 0.3903E+03 0.3928E+03 9 1.52 750.39 750.88 0.4087E+03 0.3907E+03 11 2.00 946.72 937.84 0.3896E+03 0.3862E+03 13 2.58 1159.33 1157.14 0.3664E+03 0.3673E+03 15 3.16 1357.83 1362.44 0.3153E+03 0.3357E+03 17 3.75 1542.23 1547.19 0.2924E+03 0.2947E+03 19 4.37 1710.57 1716.70 0.2679E+03 0.2440E+03 21 4.99 1855.69 1850.09 0.2049E+03 0.1920E+03 23 5.92 1996.28 1992.72 0.9100E+02 0.1160E+03 25 7.63 2050.41 2053.93 -0.8921E+00 -0.1314E+02 27 8.96 2004.13 2004.06 -0.7597E+02 -0.5670E+02 29 10.21 1854.91 1840.10 -0.1350E+03 -0.1376E+03 31 10.72 1757.43 1769.53 -0.2182E+03 -0.1398E+03 33 11.60 1621.23 1645.88 -0.1250E+03 -0.1394E+03 35 12.73 1520.19 1491.89 -0.3978E+01 -0.1341E+03 37 13.64 1579.10 1567.11 0.8855E+02 0.8585E+02 39 15.49 1727.19 1737.93 0.5786E+02 0.4655E+02 41 17.02 1808.24 1815.77 0.7372E+02 0.5520E+02 43 18.23 1931.13 1940.19 0.1490E+03 0.1054E+03 45 18.95 2053.23 2016.84 0.1480E+03 0.1079E+03 47 20.27 2161.18 2161.79 0.5522E+02 0.1115E+03 49 21.40 2203.80 2216.69 0.2025E+02 -0.1429E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21332917E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.92140114E+03 -0.11106162E+05 0.79466523E+05 -0.23294081E+06 0.27759167E+06 Rj0 = 5.9800 8.9600 12.7300 15.4900 17.0200 20.8300 RKj = -0.24096718E+02 -0.64006495E+02 0.21384094E+03 -0.52055671E+02 0.44984522E+02 -0.12792020E+03


A.1 – 70

-0.11223354E+06



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 774.26 7.66 27 730.74 7.88 28 671.15 8.44 29 657.16 9.12 30 703.91 9.91 31 786.76 10.58 32 849.45 10.95 33 912.14 11.33 34 974.96 11.78 35 1037.78 12.23 36 1112.83 12.75 37 1187.89 13.28 38 1246.16 13.73 39 1304.44 14.18 40 1385.86 14.89 41 1467.28 15.60 42 1533.49 16.27 43 1599.70 16.93 44 1680.15 17.97 45 1714.53 18.61 46 1748.91 19.25 47 1756.10 19.92 48 1739.45 20.82


lu = cu =


Remark

lp = 29.5000" gb = 2.5000" nb = 1 X 10


Major parameters

S.L.Lipson (1977) A1-10


Tested by Test Id.


I - 36

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 71


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1889E+04 0.2255E+04 3 0.08 153.01 157.12 0.1887E+04 0.1652E+04 5 0.16 306.03 272.37 0.1552E+04 0.1218E+04 7 0.38 445.65 460.42 0.6290E+03 0.5809E+03 9 0.64 562.63 573.12 0.3237E+03 0.3494E+03 11 0.92 663.00 660.17 0.4114E+03 0.2984E+03 13 1.30 778.67 769.43 0.2491E+03 0.2744E+03 15 1.91 899.28 912.18 0.1617E+03 0.1852E+03 17 3.05 1040.46 1032.40 0.6715E+02 0.5251E+02 19 4.15 1084.70 1088.69 0.2036E+02 -0.3909E+02 21 5.98 1015.13 1025.87 -0.9594E+02 -0.1471E+03 23 6.86 916.72 899.87 -0.1490E+03 -0.1423E+03 25 7.43 817.78 817.36 -0.1854E+03 -0.1476E+03 27 7.88 730.74 750.06 -0.1697E+03 -0.1544E+03 29 9.12 657.16 657.33 0.1617E+02 0.4240E+02 31 10.58 786.76 797.15 0.1522E+03 0.1652E+03 33 11.33 912.14 915.56 0.1548E+03 0.1518E+03 35 12.23 1037.78 1046.16 0.1409E+03 0.1384E+03 37 13.28 1187.89 1185.05 0.1354E+03 0.1264E+03 39 14.18 1304.44 1295.64 0.1235E+03 0.1188E+03 41 15.60 1467.28 1457.99 0.1069E+03 0.1107E+03 43 16.93 1599.70 1602.07 0.9099E+02 0.1061E+03 45 18.61 1714.53 1717.45 0.5367E+02 0.1914E+02 47 19.92 1756.10 1741.63 -0.1933E+01 0.1771E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18361667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.29114720E+04 -0.19671758E+05 0.43580738E+05 -0.18655843E+04 -0.74300214E+05 Rj0 = 4.1500 5.1100 5.9800 7.4300 8.4400 9.1200 9.9200 17.9000 RKj = -0.10385205E+03 -0.67091556E+02 -0.10544885E+03 -0.34915436E+00 0.16797467E+03 0.54517160E+02 0.15362829E+03 -0.83640760E+02


A.1 – 72

0.51312782E+05



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"

------------------------------



lu = cu =


Remark

lp = 32.5000" gb = 2.5000" nb = 1 X 11


Major parameters

S.L.Lipson (1977) A1-11


Tested by Test Id.


I - 37

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 73


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.6472E+03 0.4534E+03 3 0.32 204.13 194.92 0.6470E+03 0.6798E+03 5 0.62 379.00 386.13 0.5127E+03 0.5757E+03 7 0.90 524.61 529.87 0.4556E+03 0.4391E+03 9 1.31 676.46 677.64 0.3324E+03 0.3028E+03 11 1.78 810.27 801.16 0.2606E+03 0.2338E+03 13 2.31 935.11 917.13 0.1994E+03 0.2040E+03 15 3.12 1054.34 1064.84 0.1383E+03 0.1550E+03 17 4.33 1177.23 1187.58 0.4494E+02 0.4671E+02 19 5.32 1196.93 1198.47 0.3303E+01 -0.1795E+02 21 6.74 1171.96 1147.22 -0.2848E+02 -0.4215E+02 23 8.47 1114.22 1096.48 -0.3441E+02 -0.1161E+02 25 10.11 1071.46 1105.52 0.3213E+01 0.2041E+02 27 11.58 1131.24 1147.82 0.7836E+02 0.3486E+02 29 12.94 1287.63 1276.58 0.1439E+03 0.1458E+03 31 14.08 1455.77 1441.83 0.1445E+03 0.1430E+03 33 15.22 1617.86 1602.63 0.1343E+03 0.1381E+03 35 16.46 1774.06 1769.71 0.1176E+03 0.1321E+03 37 17.61 1899.87 1918.47 0.9657E+02 0.1269E+03 39 18.79 1998.52 2000.51 0.7866E+02 0.6693E+02 41 20.65 2125.46 2119.43 0.5787E+02 0.6148E+02 ------------------------------------------------------------------------------



A.1 – 74

0.14871781E+06



: :


1) 2)

-" 1.2500"

ll = cl =

-" 1.2500"

ta = pb =

0.3750" 3.0000"

------------------------------


1/4" Fillet weld at heel, top and bottom of angle. Connection subject to moment and shear.

lu = cu =


Remark

lp = 35.5000" gb = 2.5000" nb = 1 X 12


Major parameters

S.L.Lipson (1977) A1-12


Tested by Test Id.


I - 38

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

0

4

ta

column

12

beam

pc pc pc pc qc

gc

16

20

24

28

32




8

gb

36

40

A.1 – 75


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1315E+04 0.1693E+04 3 0.20 260.43 264.52 0.1315E+04 0.1052E+04 5 0.51 508.98 515.58 0.5532E+03 0.6320E+03 7 0.94 745.63 745.73 0.5042E+03 0.4818E+03 9 1.43 966.26 969.62 0.4482E+03 0.4326E+03 11 1.94 1181.90 1180.27 0.3936E+03 0.3862E+03 13 2.48 1392.53 1372.91 0.3366E+03 0.3334E+03 15 3.24 1587.44 1598.77 0.2553E+03 0.2585E+03 17 4.40 1810.27 1832.07 0.1502E+03 0.1436E+03 19 5.88 1952.03 1937.23 0.2604E+02 0.2397E+01 21 7.22 1893.92 1874.83 -0.1153E+03 -0.8826E+02 23 8.07 1741.22 1783.41 -0.1840E+03 -0.1412E+03 25 9.51 1643.98 1643.83 -0.1456E+02 -0.1510E+02 27 11.01 1676.90 1647.26 0.6483E+02 0.1827E+02 29 12.16 1766.66 1806.07 0.1164E+03 0.1486E+03 31 13.18 1919.68 1967.09 0.2050E+03 0.1679E+03 33 13.83 2075.07 2054.37 0.2168E+03 0.1403E+03 35 14.78 2249.15 2195.51 0.1690E+03 0.1558E+03 37 16.15 2454.23 2423.09 0.1354E+03 0.1739E+03 39 17.60 2629.18 2684.77 0.1007E+03 0.1877E+03 41 19.24 2756.10 2752.85 0.6361E+02 0.4616E+02 43 20.78 2814.80 2811.45 0.2346E+02 0.4075E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20312583E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.18924539E+04 -0.23940891E+05 0.15445681E+06 -0.42886636E+06 0.50827611E+06 Rj0 = 8.0700 8.9500 10.0600 11.0100 13.1800 17.6000 19.2400 RKj = -0.19912429E+02 0.14313016E+03 0.19103347E+02 0.10988871E+03 -0.39228704E+02 -0.15187802E+03 -0.11465822E+02


A.1 – 76

-0.21095107E+06



: :


1) 2)

----

" " "

Single plate connection.

lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.

Fasteners: A325- -3/4"D 15/16" Oversize holes Material : A36 Fy = -ksi Fu = -ksi

L.E.Thompson et al. (1970) F-1 ALT

Column : W10X49 Beam : W21X62 Angle : --

Tested by Test Id.


I - 39

0

150

300

450

600

750

900

1050

1200

1350

1500

0


10

30

40

50

60


20

qc

70

pc pc pc pc

Material : A36 Fy = 36.00 ksi (nominal) : Experimental : M. Exponential

ta

column

80

gc

90

100

A.1 – 77


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1228E+03 0.1349E+03 3 0.70 85.99 85.55 0.1144E+03 0.1120E+03 5 1.40 160.22 158.79 0.9923E+02 0.9796E+02 7 2.10 224.92 223.10 0.8480E+02 0.8584E+02 9 3.20 305.03 306.90 0.6615E+02 0.6638E+02 11 4.30 370.44 369.18 0.5395E+02 0.4708E+02 13 6.60 441.00 438.56 0.1681E+02 0.1597E+02 15 11.30 477.76 477.63 0.6731E+01 0.2402E+01 17 15.57 502.25 497.53 0.5741E+01 0.5383E+01 19 20.75 523.69 526.83 0.3012E+01 0.5404E+01 21 26.13 545.12 551.80 0.5251E+01 0.3907E+01 23 30.80 569.63 568.39 0.5586E+01 0.3377E+01 25 36.90 606.37 590.22 0.3977E+01 0.3952E+01 27 42.58 618.13 615.57 0.2070E+01 0.4991E+01 29 48.26 629.89 646.73 0.2070E+01 0.5945E+01 31 53.00 657.82 676.39 0.1161E+02 0.6539E+01 33 55.70 734.26 719.95 0.6799E+02 0.7066E+02 35 57.30 846.72 833.11 0.7258E+02 0.7079E+02 37 58.90 958.44 946.46 0.6706E+02 0.7090E+02 39 60.45 1060.97 1056.42 0.6518E+02 0.7099E+02 41 61.75 1144.40 1148.75 0.6280E+02 0.7105E+02 43 63.10 1231.13 1244.71 0.6523E+02 0.7111E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.61333333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.36346292E+03 -0.73841783E+04 0.38898994E+05 -0.83901630E+05 0.83369958E+05 Rj0 = 6.6000 11.3000 55.3000 RKj = 0.56149868E+01 0.20084087E+01 0.63868948E+02


A.1 – 78

-0.31024598E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


L.E.Thompson et al. (1970) F-1 ALT


Tested by Test Id.


I - 40

0

150

300

450

600

750

900

1050

1200

1350

1500

0


11

33

44

55

66


22

qc

77

pc pc pc pc


ta

column

88

gc

99

110

A.1 – 79


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1433E+03 0.1565E+03 3 0.60 85.99 86.08 0.1335E+03 0.1319E+03 5 1.20 160.22 159.54 0.1158E+03 0.1138E+03 7 1.80 224.92 223.29 0.1003E+03 0.9912E+02 9 2.70 305.03 303.86 0.8085E+02 0.8039E+02 11 3.60 370.44 368.68 0.6396E+02 0.6399E+02 13 5.00 441.00 442.58 0.4606E+02 0.4239E+02 15 9.60 532.87 533.77 0.6578E+01 0.5279E+01 17 15.50 542.06 540.39 0.1558E+01 0.5248E+00 19 21.40 551.26 550.98 0.2001E+01 0.2761E+01 21 26.53 563.50 565.98 0.2386E+01 0.2834E+01 23 32.07 581.88 579.39 0.4129E+01 0.1954E+01 25 38.00 606.37 612.17 0.6458E+01 0.5579E+01 27 44.20 661.50 644.77 0.5151E+01 0.4999E+01 29 50.20 670.69 673.85 0.1531E+01 0.4728E+01 31 56.20 679.87 701.82 0.6098E+01 0.4613E+01 33 61.60 735.00 726.61 0.4589E+02 0.4574E+01 35 63.40 839.00 847.96 0.7023E+02 0.6741E+02 37 64.90 959.92 949.07 0.7530E+02 0.6741E+02 39 66.30 1058.40 1043.44 0.6667E+02 0.6741E+02 41 67.70 1146.60 1137.81 0.5407E+02 0.6740E+02 43 71.20 1231.13 1231.13 0.1610E+02 -0.4994E+00 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.66833333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.21526746E+03 -0.35697020E+04 0.15275399E+05 -0.22781211E+05 0.14196025E+05 Rj0 = 15.5000 32.7000 61.6000 69.1000 RKj = 0.23576865E-01 0.45387460E+01 0.62844928E+02 -0.67902244E+02


A.1 – 80

-0.27415056E+04



: :


1) 2)

----

" " "

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


lu = cu = qb =


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


L.E.Thompson et al. (1970) G-1 ALT


Tested by Test Id.


I - 41

0

150

300

450

600

750

900

1050

1200

1350

1500

0


11

33

44

55

66


22

qc

77

pc pc pc pc


ta

column

88

gc

99

110

A.1 – 81


Moment ( kip-inch )

( R : X 1/1000 radians )


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.69000000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.31620063E+03 0.10299317E+04 0.23005865E+04 -0.60054736E+04 0.30726978E+04 Rj0 = 28.7000 44.9000 55.9000 62.7000 67.1000 RKj = 0.68061454E+01 -0.53201916E+01 0.10302492E+02 0.55990565E+02 -0.63941046E+02


A.1 – 82

0.45478622E+03



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


L.E.Thompson et al. (1970) G-1 ALT


Tested by Test Id.


I - 42

0

150

300

450

600

750

900

1050

1200

1350

1500

0


11

33

44

55

66


22

qc

77

pc pc pc pc


ta

column

88

gc

99

110

A.1 – 83


Moment ( kip-inch )

( R : X 1/1000 radians )


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.65916667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.61339462E+03 0.52396380E+04 -0.19484630E+05 0.49397274E+05 -0.62163011E+05 Rj0 = 11.6000 29.8000 52.7000 66.0000 RKj = -0.83117480E+01 0.12462279E+02 -0.38694691E+01 0.79811769E+02


A.1 – 84

0.28429141E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


L.E.Thompson et al. (1970) H-1 ALT


Tested by Test Id.


I - 43

0

150

300

450

600

750

900

1050

1200

1350

1500

0


pc pc pc pc

9

27

36

45

54

63

qc


18


ta

column

72

gc

81

90

A.1 – 85


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 86

-0.18048075E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


L.E.Thompson et al. (1970) H-1 ALT


Tested by Test Id.


I - 44

0

150

300

450

600

750

900

1050

1200

1350

1500

0


11

33

44

55

66


22

qc

77

pc pc pc pc


ta

column

88

gc

99

110

A.1 – 87


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1305E+03 0.1128E+03 3 0.40 52.19 46.82 0.1278E+03 0.1198E+03 5 1.00 119.81 118.53 0.1006E+03 0.1172E+03 7 1.70 196.25 196.43 0.1086E+03 0.1042E+03 9 2.50 267.17 272.25 0.8636E+02 0.8510E+02 11 3.40 338.83 339.27 0.7130E+02 0.6425E+02 13 4.35 393.96 391.21 0.4736E+02 0.4579E+02 15 5.70 442.46 439.18 0.2580E+02 0.2657E+02 17 11.97 479.23 484.00 0.1438E+01 -0.1342E+01 19 18.10 488.05 480.42 0.1438E+01 0.1338E+01 21 24.23 496.87 500.92 0.1438E+01 0.4864E+01 23 29.45 527.36 528.66 0.1213E+02 0.5440E+01 25 34.10 579.91 576.19 0.1058E+02 0.1061E+02 27 39.75 633.94 632.17 0.8750E+01 0.9174E+01 29 45.43 679.88 680.31 0.7254E+01 0.7816E+01 31 50.50 716.63 717.46 0.4738E+01 0.6896E+01 33 57.15 726.18 727.66 0.1436E+01 0.1175E+01 35 63.80 735.73 733.85 0.6430E+01 0.7323E+00 37 67.55 784.98 783.47 0.1709E+02 0.1316E+02 39 72.30 840.47 845.67 0.8234E+01 0.1304E+02 ------------------------------------------------------------------------------



A.1 – 88

0.24261064E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


L.E.Thompson et al. (1970) F-2-1 ALT


Tested by Test Id.


I - 45

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0


14

42

56

70

84

gc

112 126 140 Rotation ( x 1/1000 radians )

28

qc

98

pc pc pc pc


ta

column

A.1 – 89


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1249E+03 0.1346E+03 3 0.70 83.80 78.82 0.1006E+03 0.9266E+02 5 1.80 150.67 154.56 0.4213E+02 0.4913E+02 7 4.50 221.23 224.62 0.2036E+02 0.1463E+02 9 8.50 293.27 288.82 0.1766E+02 0.1947E+02 11 12.70 373.38 374.68 0.1703E+02 0.1949E+02 13 17.10 441.00 446.48 0.1495E+02 0.1300E+02 15 22.90 515.23 510.17 0.1164E+02 0.1011E+02 17 29.70 585.06 576.74 0.8395E+01 0.1004E+02 19 35.70 630.01 639.50 0.7492E+01 0.1076E+02 21 41.30 698.26 699.33 0.1394E+02 0.1044E+02 23 45.80 746.76 744.46 0.7777E+01 0.9551E+01 25 53.55 766.97 757.59 0.2608E+01 0.6463E+00 27 61.30 787.19 754.93 0.2188E+02 -0.1259E+01 29 65.40 934.92 1012.13 0.8449E+05 0.6234E+02 31 66.80 1108.38 1099.24 0.6424E+02 0.6211E+02 33 69.10 1254.65 1241.67 0.6064E+02 0.6175E+02 35 71.70 1400.92 1401.78 0.5171E+02 0.6141E+02 37 75.10 1543.36 1542.68 0.3515E+02 0.2742E+02 39 79.90 1688.29 1673.29 0.2625E+02 0.2702E+02 41 86.80 1840.44 1858.36 0.1967E+02 0.2665E+02 ------------------------------------------------------------------------------



A.1 – 90

0.60389800E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.




Tested by Test Id.


I - 46

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0


pc pc pc pc

16

48

64

80

96

gc

112 128 144 160

qc


32


ta

column

A.1 – 91


Moment ( kip-inch )

( R : X 1/1000 radians )


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.96500000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.49064675E+02 0.51202398E+04 -0.32048176E+05 0.88121944E+05 -0.10948755E+06 Rj0 = 13.4000 54.7000 74.8000 86.8000 RKj = -0.42630341E+00 -0.24887472E+01 0.57424653E+02 -0.28677574E+02


A.1 – 92

0.49171071E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.




Tested by Test Id.


I - 47

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

14

ta

column

42

beam

pc pc pc pc qc

gc

56

70

84

98

112 126 140




28

gb

A.1 – 93


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.5144E+03 0.1878E+03 3 0.80 121.27 125.83 0.1087E+03 0.1293E+03 5 2.30 260.93 260.36 0.6408E+02 0.5775E+02 7 7.95 367.87 366.02 0.1087E+02 0.9207E+01 9 14.30 442.47 443.09 0.1286E+02 0.1348E+02 11 20.05 514.87 517.54 0.1233E+02 0.1234E+02 13 25.80 588.01 586.61 0.1312E+02 0.1179E+02 15 32.10 671.80 659.00 0.9609E+01 0.1105E+02 17 40.63 713.93 718.35 0.4938E+01 -0.3306E+01 19 46.45 788.29 794.97 0.3438E+02 0.6039E+02 21 49.10 922.43 953.79 0.7832E+02 0.5948E+02 23 50.50 1036.36 1036.74 0.7781E+02 0.5902E+02 25 52.00 1147.33 1124.92 0.6838E+02 0.5856E+02 27 53.80 1258.32 1229.85 0.5526E+02 0.5804E+02 29 56.00 1362.68 1356.89 0.4472E+02 0.5746E+02 31 58.70 1474.42 1511.16 0.3823E+02 0.5683E+02 33 61.80 1581.72 1589.94 0.3262E+02 0.2512E+02 35 66.20 1728.72 1698.92 0.3266E+02 0.2445E+02 37 71.20 1837.50 1819.69 0.1972E+02 0.2390E+02 39 75.20 1911.00 1914.63 0.1612E+02 0.2359E+02 41 81.10 1984.50 1996.05 0.1056E+02 0.4970E+01 43 89.70 2035.96 2037.63 0.2673E+01 0.4729E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.77250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.27697160E+03 0.82633999E+04 -0.42811640E+05 0.10292462E+06 -0.11464514E+06 Rj0 = 38.5000 44.9000 58.7000 78.0000 RKj = -0.11862347E+02 0.65817205E+02 -0.31107630E+02 -0.18313086E+02


A.1 – 94

0.47422691E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.




Tested by Test Id.


I - 48

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

14

ta

column

42

beam

pc pc pc pc qc

gc

56

70

84

98

112 126 140




28

gb

A.1 – 95


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 96

0.35320167E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------


ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.




Tested by Test Id.


I - 49

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

15

ta

column

45

beam

pc pc pc pc qc

gc

60

75

90

105 120 135 150




30

gb

A.1 – 97


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2168E+03 0.1896E+03 3 1.00 129.36 126.23 0.8537E+02 0.7740E+02 5 5.90 221.98 216.56 0.1260E+02 0.1057E+02 7 13.50 330.76 335.26 0.1586E+02 0.1574E+02 9 20.45 437.69 437.24 0.1369E+02 0.1443E+02 11 25.60 511.93 513.84 0.1512E+02 0.1533E+02 13 32.40 624.76 619.25 0.1711E+02 0.1529E+02 15 40.90 738.68 738.52 0.9859E+01 0.1239E+02 17 49.10 819.52 834.33 0.9859E+01 0.1098E+02 19 54.20 954.77 949.18 0.8910E+02 0.7329E+02 21 55.80 1090.01 1065.96 0.7519E+02 0.7269E+02 23 58.35 1234.80 1250.20 0.5725E+02 0.7183E+02 25 60.40 1344.68 1380.45 0.5045E+02 0.3035E+02 27 62.80 1454.38 1452.50 0.4170E+02 0.2970E+02 29 65.65 1560.22 1536.17 0.3331E+02 0.2903E+02 31 69.30 1665.51 1640.81 0.2555E+02 0.2833E+02 33 74.90 1802.95 1797.07 0.2027E+02 0.2753E+02 35 78.80 1874.99 1903.61 0.1721E+02 0.2713E+02 37 84.10 1950.70 1953.81 0.1154E+02 0.4184E+01 39 91.55 1997.20 1983.60 0.2964E+01 0.3847E+01 41 97.80 1984.50 2007.10 -0.9046E+01 0.3684E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.86500000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.80803403E+03 -0.44478488E+03 -0.18015560E+05 0.71838664E+05 -0.10020157E+06 Rj0 = 45.0000 53.2000 60.0000 80.0000 RKj = 0.24044333E+01 0.64449177E+02 -0.40845677E+02 -0.22554838E+02


A.1 – 98

0.46968989E+05



: :


1) 2)

----

" " "


lu = cu = qb =

ta =

0.6250"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 1719.17 83.70 27 1797.08 87.40 28 1874.99 91.10 29 1912.84 94.10 30 1950.70 97.10 31 1969.80 100.97 32 1988.91 104.83 33 2008.02 108.70 34 1984.50 111.70

ll = -" cl = -" nb = 2 X -

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.




Tested by Test Id.


I - 50

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

17

ta

column

51

beam

pc pc pc pc qc

gc

68

85

102 119 136 153 170




34

gb

A.1 – 99


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2168E+03 0.1751E+03 3 1.10 129.36 135.13 0.8291E+02 0.8109E+02 5 7.28 240.72 242.39 0.1005E+02 0.5675E+01 7 18.02 348.76 349.79 0.1005E+02 0.1086E+02 9 27.80 472.61 468.06 0.1553E+02 0.1403E+02 11 37.60 624.76 620.80 0.1537E+02 0.1636E+02 13 47.20 762.67 770.26 0.1400E+02 0.1419E+02 15 56.40 891.49 883.14 0.1028E+02 0.1026E+02 17 66.90 954.77 954.02 0.4609E+02 0.4777E+01 19 69.98 1132.93 1133.42 0.5784E+02 0.5777E+02 21 73.06 1311.09 1310.02 0.5784E+02 0.5692E+02 23 76.88 1479.92 1480.69 0.3505E+02 0.3637E+02 25 81.42 1639.42 1644.13 0.3505E+02 0.3551E+02 27 87.40 1797.08 1792.54 0.2106E+02 0.1815E+02 29 94.10 1912.84 1911.89 0.1262E+02 0.1752E+02 31 100.97 1969.80 1974.16 0.4942E+01 0.2495E+01 33 108.70 2008.02 1992.25 -0.2256E+01 0.2208E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.98083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.50880834E+03 0.42427865E+04 -0.43606708E+05 0.13570385E+06 -0.17139460E+06 Rj0 = 56.4000 66.9000 74.6000 83.7000 97.1000 RKj = -0.13450369E+01 0.53964771E+02 -0.19664025E+02 -0.16519067E+02 -0.14603391E+02


A.1 – 100

0.75610514E+05




: :

1) 2)

" "


---

---

" "

ta = pb =

0.2500" 3.0000"

------------------------------


ll = cl =

Major parameters


Remark

lu = cu =

U.S.A.


R.M.Richard et al. (1982) RGKL2

lp = 6.0000" gb = -" nb = 1 X 2

Column : -Beam : -Angle : --

Tested by Test Id.


I - 51

0

10

20

30

40

50

60

70

80

90

100

0


9

27

36

45

54


18

qc

63

pc pc pc pc


ta

column

72

gc

81

90

A.1 – 101


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.7304E+01 0.2499E+01 3 0.53 3.90 3.20 0.7305E+01 0.8389E+01 5 1.12 8.46 8.61 0.8249E+01 0.9563E+01 7 1.75 13.68 14.34 0.8248E+01 0.8305E+01 9 2.38 18.90 18.99 0.8249E+01 0.6364E+01 11 3.20 23.32 23.23 0.3616E+01 0.4128E+01 13 4.20 26.94 26.38 0.3180E+01 0.2342E+01 15 9.10 32.06 32.06 0.8578E+00 0.8337E+00 17 14.30 35.49 35.63 0.6585E+00 0.5388E+00 19 18.90 38.15 37.86 0.4740E+00 0.4640E+00 21 22.90 40.04 39.75 0.4155E+00 0.4841E+00 23 27.90 41.76 42.14 0.3424E+00 0.4548E+00 25 33.04 43.69 44.23 0.4100E+00 0.3543E+00 27 38.32 45.86 45.79 0.4100E+00 0.2364E+00 29 43.60 48.02 47.81 0.4600E+00 0.5420E+00 31 48.13 50.30 50.14 0.5029E+00 0.4865E+00 33 52.67 52.30 52.25 0.3776E+00 0.4506E+00 35 57.20 54.01 54.24 0.3776E+00 0.4287E+00 ------------------------------------------------------------------------------



A.1 – 102

0.24209010E+04



: :


1) 2)

" "


---

---

" "

ta = pb =

0.2500" 3.0000"

------------------------------


ll = cl =

Major parameters


Remark

lu = cu =

U.S.A.



lp = 9.0000" gb = -" nb = 1 X 3


Tested by Test Id.


I - 52

0

20

40

60

80

100

120

140

160

180

200

0

10

ta

column

30

beam

pc pc pc pc qc

gc

40

50

60

70

80

90

100




20

gb

A.1 – 103


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 104

0.29996436E+04



: :


1) 2)

" "


---

---

" "

ta = pb =

0.2500" 3.0000"

------------------------------


ll = cl =

Major parameters


Remark

lu = cu =

U.S.A.



lp = 15.0000" gb = -" nb = 1 X 5


Tested by Test Id.


I - 53

0

75

150

225

300

375

450

525

600

675

750

0

9

ta

column

27

beam

pc pc pc pc qc

gc

36

45

54

63

72

81




18

gb

90

A.1 – 105


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 106

0.36704670E+03



: :


1) 2)

" "


---

---

" "

ta = pb =

0.3750" 3.0000"

------------------------------


ll = cl =

Major parameters


Remark

lu = cu =

U.S.A.

Fasteners: A325- -7/8"D 1 1/16" Oversize holes Material : A36 Fy = -ksi Fu = -ksi


lp = 21.5000" gb = -" nb = 1 X 7


Tested by Test Id.


I - 54

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

10

ta

column

30

beam

pc pc pc pc qc

gc

40

50

60

70

80

90

100




20

gb

A.1 – 107


Moment ( kip-inch )

( R : X 1/1000 radians )




A.1 – 108

0.57968144E+04



: :


1) 2)

lu = 1.7500" gc = 2.6250" nb = 2 X 1

ll = 1.7500" cu = 1.2500" nc = 1 X 1

ta = cl =

II -

0.3750" 1.2500"

------------------------------


Connection angle riveted to 1/2" mounting plate.

2.5000" 3.5000" 2.5000"


Remark

lp = gb = qb =

U.S.A. Fasteners: 10.9-X-7/8"D 15/16" Oversize holes Material : -Fy = 44.00 ksi Fu = 64.80 ksi

Major parameters

J.C.Rathbun (1936) A-1

Column : -Beam : W6X12.5 Angle : 6 X 4 X 3/8

Tested by Test Id.

Connection type : Double web-angle connections Mode : All riveted

1

0

3

6

9

12

15

18

21

24

27

30

0

5

ta

column

15

beam pc pc pc pc qc

gc

20

25

30

35

40

45

Material : -Fy = 44.00 ksi : Experimental : Polynominal : M. Exponential : Power model, n = 1.81



10

gb

50

A.2 – 1


Moment ( kip-inch )

R t A3 P3

= Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.375000" = 4.570000 K = 0.845282 = 5 Q1 = -1 Q2 =

( R : X 1/1000 radians )

-3

Q3 =



0.11169381E+04

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.39904000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = -0.56289577E+01 0.10550336E+03 -0.69927895E+03 0.19892423E+04 -0.24849135E+04



A.2 – 2


: :


1) 2)

lu gc pc nc

= 1.0000" = 2.6250" = 3.0000" = 1 X 2

ll = cu = qb =

1.0000" 1.5000" 2.5000"

ta = cl =

II -

0.3750" 1.5000"

------------------------------


Connection angle riveted to 1/2" mouning plate.

= 6.0000" = 3.5000" = 3.0000" = 2 X 2


Remark

lp gb pb nb


Major parameters



Tested by Test Id.


2

0

15

30

45

60

75

90

105

120

135

150

0

4

ta

column

12

beam pc pc pc pc qc

gc

16

20

24

28

32

36




8

gb

40

A.2 – 3


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.58975965E+04

-5






A.2 – 4


: :


1) 2)

lu gc pc nc

= 1.0000" = 3.6250" = 3.0000" = 2 X 2

ll = cu = qb =

1.0000" 1.5000" 2.5000"

ta = cl = qc =

II -

0.3750" 1.5000" 2.5000"

------------------------------



= 6.0000" = 3.5000" = 3.0000" = 2 X 2


Remark

lp gb pb nb


Major parameters



Tested by Test Id.


3

0

20

40

60

80

100

120

140

160

180

200

0

5

ta

column

15

beam pc pc pc pc qc

gc

20

25

30

35

40

45




10

gb

50

A.2 – 5


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.78929535E+03

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2751E+02 0.2522E+02 0.3399E+02 0.1412E+02 3 0.35 9.72 8.88 9.54 4.98 0.2391E+02 0.2499E+02 0.2187E+02 0.1405E+02 5 0.90 19.80 22.30 19.56 12.64 0.1665E+02 0.2344E+02 0.1589E+02 0.1375E+02 7 1.59 29.76 36.98 29.54 21.84 0.1344E+02 0.1923E+02 0.1357E+02 0.1316E+02 9 2.40 39.60 50.34 39.66 32.21 0.1113E+02 0.1377E+02 0.1126E+02 0.1226E+02 11 3.41 49.69 61.86 49.75 44.00 0.9269E+01 0.9408E+01 0.8822E+01 0.1100E+02 13 4.59 59.66 71.17 59.12 56.07 0.7601E+01 0.6699E+01 0.7316E+01 0.9495E+01 15 6.13 69.64 79.91 69.75 69.27 0.6444E+01 0.4841E+01 0.6590E+01 0.7682E+01 17 7.71 79.73 86.62 79.67 80.09 0.5991E+01 0.3782E+01 0.5972E+01 0.6124E+01 19 9.55 89.83 92.83 89.70 89.97 0.4867E+01 0.3027E+01 0.4883E+01 0.4697E+01 21 12.11 100.06 99.69 99.99 100.08 0.3199E+01 0.2383E+01 0.3164E+01 0.3284E+01 23 14.28 105.56 104.46 105.51 106.28 0.2321E+01 0.2028E+01 0.1983E+01 0.2468E+01 25 16.29 109.83 108.28 108.68 110.66 0.1765E+01 0.1788E+01 0.2226E+01 0.1925E+01 27 18.69 113.02 112.29 113.27 114.68 0.1332E+01 0.1571E+01 0.1660E+01 0.1461E+01 29 21.25 116.33 116.08 117.06 117.95 0.1256E+01 0.1394E+01 0.1329E+01 0.1111E+01 31 23.77 119.89 119.42 120.17 120.43 0.1593E+01 0.1258E+01 0.1163E+01 0.8665E+00 33 26.29 123.38 122.45 122.99 122.38 0.1212E+01 0.1148E+01 0.1081E+01 0.6879E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.27465500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.44964010E+02 -0.45051047E+03 0.15995959E+04 -0.18351364E+04 -0.35014526E+02 Rj0 = 16.2900 RKj = 0.10051603E+01



A.2 – 6


: :


1) 2)

lu = gc = pc =

1.5000" 2.5625" 3.0000"

ll = 1.5000" cu = 1.5000" nb = 1 X 3

II -

ta = 0.3750" cl = 1.5000" nc = 1 X 3

------------------------------



9.0000" 2.2500" 3.0000"


Remark

lp = gb = pb =


Major parameters


Column : -Beam : W12X31.8 Angle : 4 X 3 1/2 X 3/8

Tested by Test Id.


4

0

25

50

75

100

125

150

175

200

225

250

0

4

ta

column

12

beam pc pc pc pc qc

gc

16

20

24

28

32

36




8

gb

40

A.2 – 7


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.23641637E+04

-5






A.2 – 8


: :


1) 2)

lu gc pc nc

= 1.5000" = 3.5625" = 3.0000" = 2 X 3

ll = cu = qb =

1.5000" 1.5000" 2.5000"

ta = cl = qc =

II -

0.3750" 1.5000" 2.5000"

------------------------------



= 9.0000" = 3.5000" = 3.0000" = 2 X 3


Remark

lp gb pb nb


Major parameters



Tested by Test Id.


5

0

35

70

105

140

175

210

245

280

315

350

0

4

ta

column

12

beam pc pc pc pc qc

gc

16

20

24

28

32

36




8

gb

40

A.2 – 9


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.18643013E+04

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20832833E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.18228595E+03 -0.74560665E+03 0.16399778E+04 -0.73894153E+03 -0.19767307E+04 Rj0 = 8.4700 12.7600 RKj = 0.25688439E+01 0.11517704E+01



A.2 – 10


: :


1) 2)

1.5000" 2.5000" 3.0000"

ll = 1.5000" cu = 1.5000" nb = 1 X 5

II -

ta = 0.3750" cl = 1.5000" nc = 1 X 5

------------------------------



lu = gc = pc =


Remark

lp = 15.0000" gb = 2.2500" pb = 3.0000"


Major parameters


Column : -Beam : W18X54.7 Angle : 4 X 3 1/2 X 3/8

Tested by Test Id.


6

0

55

110

165

220

275

330

385

440

495

550

0

2

ta

column

6

beam pc pc pc pc qc

gc

8

10

12

14

16

18




4

gb

20

A.2 – 11


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.19261428E+05

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.96163333E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.17530126E+02 0.22299255E+04 -0.14727152E+05 0.38949631E+05 -0.45275720E+05 Rj0 = 6.6000 RKj = 0.10789658E+02



A.2 – 12


: :


1) 2)

lu gc pc nc

= 1.5000" = 3.5000" = 3.0000" = 2 X 5

ll = cu = qb =

1.5000" 1.5000" 2.5000"

ta = cl = qc =

II -

0.3750" 1.5000" 2.5000"

------------------------------



= 15.0000" = 3.5000" = 3.0000" = 2 X 5


Remark

lp gb pb nb


Major parameters



Tested by Test Id.


7

0

75

150

225

300

375

450

525

600

675

750

0

1

ta

column

3

beam pc pc pc pc qc

gc

4

5

6

7

8

9




2

gb

10

A.2 – 13


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.19199228E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3886E+03 0.2274E+03 0.3495E+03 0.2685E+03 3 0.13 49.67 29.09 47.87 33.13 0.3590E+03 0.2272E+03 0.3747E+03 0.2500E+03 5 0.28 98.76 63.40 100.23 69.44 0.3082E+03 0.2262E+03 0.3133E+03 0.2306E+03 7 0.45 149.41 102.88 148.68 108.10 0.2599E+03 0.2239E+03 0.2432E+03 0.2110E+03 9 0.68 200.50 153.86 197.42 154.07 0.1935E+03 0.2188E+03 0.1858E+03 0.1888E+03 11 1.01 250.37 223.01 249.99 210.97 0.1394E+03 0.2068E+03 0.1431E+03 0.1632E+03 13 1.42 300.10 303.45 302.15 272.47 0.1175E+03 0.1841E+03 0.1141E+03 0.1376E+03 15 1.86 350.31 378.53 348.58 328.37 0.1050E+03 0.1556E+03 0.9779E+02 0.1163E+03 17 2.39 400.37 452.31 397.06 384.42 0.8258E+02 0.1248E+03 0.8628E+02 0.9678E+02 19 2.86 434.25 505.99 435.47 426.84 0.7168E+02 0.1034E+03 0.7594E+02 0.8321E+02 21 3.36 467.21 553.08 470.16 465.36 0.6109E+02 0.8639E+02 0.6296E+02 0.7179E+02 23 3.88 499.24 594.74 499.37 500.38 0.5564E+02 0.7319E+02 0.4850E+02 0.6214E+02 25 4.48 528.51 634.61 523.56 534.46 0.4489E+02 0.6220E+02 0.3373E+02 0.5343E+02 27 4.95 547.89 662.21 548.01 558.20 0.4038E+02 0.5552E+02 0.4764E+02 0.4776E+02 29 5.62 574.36 697.14 576.64 588.17 0.3800E+02 0.4807E+02 0.3769E+02 0.4105E+02 31 6.28 598.74 726.96 599.33 613.47 0.3478E+02 0.4251E+02 0.3155E+02 0.3579E+02 33 6.77 614.91 746.84 613.95 630.09 0.3320E+02 0.3919E+02 0.2867E+02 0.3253E+02 ----------------------------------------------------------------------------------------------------------------------------





A.2 – 14


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.5730" = 3.0000" = 1 X 4

ll = cu = qb =

3.2500" 1.2500" 3.0000"

ta = cl =

0.3750" 1.2500"

II -

8

------------------------------


High strength bolts used Bolts : Fy=87.9 ksi, Fu=136.6 ksi, Rivets : Fy=36.5 ksi, Fu=63.2 ksi

= 11.5000" = 4.5000" = 3.0000" = 2 X 4


Remark

lp gb pb nb

U.S.A. Fasteners: A325- -3/4"D 13/16" Oversize holes Material : -Fy = 38.10 ksi Fu = 64.50 ksi

Major parameters

W.G.Bell et al. (1958) FK-4A

Column : W12X65 Beam : W18X50 Angle : 6 X 4 X 3/8

Tested by Test Id.

Connection type : Double web-angle connections Mode : Riveted-to-beam and bolted-to-column

0

60

120

180

240

300

360

420

480

540

600

0

11

ta

column

33

beam pc pc pc pc qc

gc

44

55

66

77

88

99




22

gb

110

A.2 – 15


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



-0.20332224E+04

-5






A.2 – 16


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.5730" = 3.0000" = 1 X 4

ll = cu = qb =

3.2500" 1.2500" 3.0000"

ta = cl =

0.3750" 1.2500"

II -

9

------------------------------



= 11.5000" = 4.5000" = 3.0000" = 2 X 4


Remark

lp gb pb nb


Major parameters

W.G.Bell et al. (1958) FK-4B


Tested by Test Id.


0

55

110

165

220

275

330

385

440

495

550

0

12

ta

column

36

beam pc pc pc pc qc

gc

48

60

72

84

96

108 120




24

gb

A.2 – 17


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



-0.64964724E+04

-5






A.2 – 18


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.5730" = 3.0000" = 1 X 4

ll = cu = qb =

3.2500" 1.2500" 3.0000"

ta = cl =

0.3750" 1.2500"

II - 10

------------------------------



= 11.5000" = 4.5000" = 3.0000" = 2 X 4


Remark

lp gb pb nb


Major parameters

W.G.Bell et al. (1958) FK-4C


Tested by Test Id.


0

70

140

210

280

350

420

490

560

630

700

0

13

ta

column

39

beam pc pc pc pc qc

gc

52

65

78

91

104 117 130




26

gb

A.2 – 19


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



-0.20432854E+05

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.85040917E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.43582679E+03 -0.71415566E+04 0.33242691E+05 -0.66136249E+05 0.60354956E+05 Rj0 = 35.7700 41.4800 RKj = 0.76301928E+01 -0.29302073E+01



A.2 – 20


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.5730" = 3.0000" = 1 X 4

ll = cu = qb =

3.2500" 1.2500" 3.0000"

ta = cl =

0.3750" 1.2500"

II - 11

------------------------------



= 11.5000" = 4.5000" = 3.0000" = 2 X 4


Remark

lp gb pb nb


Major parameters

W.G.Bell et al. (1958) FK-4R


Tested by Test Id.


0

55

110

165

220

275

330

385

440

495

550

0

14

ta

column

42

beam pc pc pc pc qc

gc

56

70

84

98

112 126 140




28

gb

A.2 – 21


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.11607501E+05

-5






A.2 – 22


: :


1) 2)

lu gc pc nc

= 1.7500" = 2.6320" = 3.0000" = 1 X 3

High strength bolts used

= 8.5000" = 3.5000" = 3.0000" = 2 X 3

1.7500" 1.2500" 2.5000"

ta = cl =

II - 12

0.3750" 1.2500"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.

Fasteners: A325- -3/4"D 13/16" Oversize holes Material : -Fy = 40.30 ksi Fu = 64.00 ksi

C.W.Lewitt et al. (1966) FK-3


Tested by Test Id.


0

30

60

90

120

150

180

210

240

270

300

0

13

ta

column

39

beam pc pc pc pc qc

gc

52

65

78

91

104 117 130




26

gb

A.2 – 23


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.28537063E+03

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.76157333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.16769802E+03 -0.48028817E+03 0.10266017E+04 -0.72048023E+03 -0.14632101E+03 Rj0 = 4.1400 14.3300 24.0000 RKj = 0.15305401E+01 0.26467909E+00 -0.57159894E+00



A.2 – 24


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.0710" = 3.0000" = 2 X 4

No washers used. High strength bolts used

= 11.5000" = 3.5000" = 3.0000" = 2 X 4

3.2500" 1.2500" 2.5000"

ta = cl = qc =

II - 13

0.3750" 1.2500" 2.0000"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.


C.W.Lewitt et al. (1966) FK-4AB-M


Tested by Test Id.

Connection type : Double web-angle connections Mode : All bolted

0

60

120

180

240

300

360

420

480

540

600

0

12

ta

column

36

beam pc pc pc pc qc

gc

48

60

72

84

96

Material : -Fy = 41.60 ksi : Experimental : Polynominal : M. Exponential



24

gb

108 120

A.2 – 25


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =

© 2011 J. Ross Publishing, Inc. -0.63397921E+04

-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1046E+03 0.1298E+03 0.8275E+02 3 0.46 39.70 59.86 34.43 0.6209E+02 0.1277E+03 0.6680E+02 5 1.23 78.93 152.36 78.66 0.5728E+02 0.1116E+03 0.5059E+02 7 2.19 120.68 243.21 121.30 0.4037E+02 0.7742E+02 0.3922E+02 9 3.30 160.94 312.65 160.16 0.3246E+02 0.5030E+02 0.3118E+02 11 4.66 200.72 368.61 197.62 0.2651E+02 0.3387E+02 0.2413E+02 13 6.82 241.08 427.37 240.39 0.1607E+02 0.2217E+02 0.1599E+02 15 10.33 282.57 489.39 281.76 0.9793E+01 0.1436E+02 0.8608E+01 17 16.64 321.29 560.32 318.73 0.5162E+01 0.9012E+01 0.3999E+01 19 23.04 347.98 609.62 348.65 0.4169E+01 0.6658E+01 0.3578E+01 21 29.48 369.04 647.86 369.09 0.2385E+01 0.5328E+01 0.2925E+01 23 35.96 384.49 679.40 385.76 0.2385E+01 0.4466E+01 0.2342E+01 25 42.44 399.94 706.27 400.53 0.2432E+01 0.3863E+01 0.2268E+01 27 49.07 416.41 730.31 415.90 0.2481E+01 0.3405E+01 0.2376E+01 29 55.71 432.87 751.69 432.09 0.2481E+01 0.3052E+01 0.2501E+01 31 62.04 448.71 770.13 448.21 0.2526E+01 0.2784E+01 0.2588E+01 33 68.05 463.91 786.23 463.96 0.2526E+01 0.2573E+01 0.2641E+01 35 74.07 479.12 801.16 479.96 0.2526E+01 0.2394E+01 0.2672E+01 --------------------------------------------------------------------------------------------------




A.2 – 26


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.0710" = 3.0000" = 2 X 4

High strength bolts used

= 11.5000" = 3.5000" = 3.0000" = 2 X 4

3.2500" 1.2500" 2.5000"

ta = cl = qc =

II - 14

0.3750" 1.2500" 2.0000"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.


C.W.Lewitt et al. (1966) FK-4P


Tested by Test Id.


0

55

110

165

220

275

330

385

440

495

550

0

10

ta

column

30

beam pc pc pc pc qc

gc

40

50

60

70

80




20

gb

90

100

A.2 – 27


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7816E+02 0.1298E+03 0.1038E+03 2 0.24 18.52 30.70 22.72 0.1967E+03 0.1293E+03 0.8855E+02 3 0.32 39.02 41.77 30.09 0.2076E+03 0.1288E+03 0.8375E+02 4 0.76 58.55 96.96 62.05 0.4715E+02 0.1236E+03 0.6403E+02 5 1.14 77.58 143.04 84.26 0.9064E+02 0.1142E+03 0.5159E+02 6 1.33 98.09 163.68 93.39 0.9194E+02 0.1082E+03 0.4686E+02 7 1.87 118.63 216.45 115.50 0.3369E+02 0.8859E+02 0.3648E+02 8 2.60 138.68 272.52 138.73 0.2494E+02 0.6532E+02 0.2746E+02 9 3.54 159.25 323.99 160.97 0.2120E+02 0.4652E+02 0.2072E+02 10 4.52 179.32 363.83 179.10 0.1751E+02 0.3505E+02 0.1640E+02 11 6.01 198.92 407.93 200.19 0.1337E+02 0.2549E+02 0.1235E+02 12 7.49 219.02 441.49 216.51 0.1135E+02 0.2005E+02 0.9797E+01 13 10.28 239.22 488.55 239.51 0.6448E+01 0.1445E+02 0.7049E+01 14 12.55 252.38 518.23 254.00 0.5790E+01 0.1183E+02 0.5796E+01 15 14.82 265.54 542.98 266.11 0.5790E+01 0.1007E+02 0.4890E+01 16 17.09 278.70 564.33 276.33 0.4962E+01 0.8787E+01 0.5527E+01 17 19.61 288.87 585.04 289.22 0.4044E+01 0.7726E+01 0.4734E+01 18 22.13 299.05 603.41 300.21 0.4044E+01 0.6910E+01 0.4014E+01 19 24.64 309.23 619.96 309.50 0.4044E+01 0.6263E+01 0.3388E+01 20 27.16 319.40 635.03 317.35 0.3707E+01 0.5735E+01 0.2871E+01 21 30.00 328.85 650.61 328.77 0.3325E+01 0.5245E+01 0.3804E+01 22 32.84 338.30 664.91 339.08 0.3325E+01 0.4839E+01 0.3470E+01 23 35.68 347.75 678.16 348.59 0.3325E+01 0.4496E+01 0.3235E+01 24 38.52 357.20 690.51 357.54 0.3172E+01 0.4203E+01 0.3075E+01 25 41.82 367.05 703.86 367.45 0.2995E+01 0.3912E+01 0.2957E+01 26 45.11 376.91 716.31 377.05 0.2995E+01 0.3663E+01 0.2886E+01 27 48.40 386.76 728.00 386.48 0.2995E+01 0.3446E+01 0.2846E+01 28 51.69 396.62 739.02 395.80 0.2850E+01 0.3256E+01 0.2823E+01 29 54.63 404.63 748.37 404.10 0.2721E+01 0.3104E+01 0.2813E+01 30 57.57 412.63 757.30 412.36 0.2721E+01 0.2967E+01 0.2807E+01 31 60.52 420.64 765.85 420.62 0.2721E+01 0.2843E+01 0.2804E+01 32 63.46 428.64 774.22 428.86 0.2721E+01 0.2728E+01 0.2803E+01 33 66.40 436.65 781.93 437.11 0.2721E+01 0.2627E+01 0.2802E+01 --------------------------------------------------------------------------------------------------




A.2 – 28


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.5710" = 3.0000" = 1 X 4


= 11.5000" = 3.5000" = 3.0000" = 2 X 4

3.2500" 1.2500" 2.5000"

ta = cl =

II - 15

0.3750" 1.2500"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.


C.W.Lewitt et al. (1966) WK-4


Tested by Test Id.


0

55

110

165

220

275

330

385

440

495

550

0

12

ta

column

36

beam pc pc pc pc qc

gc

48

60

72

84

96

108 120




24

gb

A.2 – 29


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



-0.10405301E+05

-5






A.2 – 30


: :


1) 2)

3.2500" 2.5710" 3.0000"


lu = gc = pc =

II - 16

ta = 0.3750" cl = 1.2500" nc = 1 X 4

------------------------------


ll = 3.2500" cu = 1.2500" nb = 1 X 4

Major parameters


Remark

lp = 11.5000" gb = 2.2500" pb = 3.0000"

U.S.A.


C.W.Lewitt et al. (1966) FB-4

Column : W12X65 Beam : W18X50 Angle : 6 X 3.5 X 3/8

Tested by Test Id.


0

55

110

165

220

275

330

385

440

495

550

0

11

ta

column

33

beam pc pc pc pc qc

gc

44

55

66

77

88

99




22

gb

110

A.2 – 31


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.81312216E+04

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.63440833E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.76606601E+02 0.14280102E+04 -0.90745485E+04 0.21724215E+05 -0.21977329E+05 Rj0 = 12.8800 24.5900 RKj = 0.28820759E+01 -0.77923603E+00



A.2 – 32


: :


1) 2)

lu gc pc nc

= 3.2500" = 2.5500" = 3.0000" = 1 X 5

No washers used.

= 14.5000" = 3.5000" = 3.0000" = 2 X 5

3.2500" 1.2500" 2.5000"

ta = cl =

II - 17

0.4380" 1.2500"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.


C.W.Lewitt et al. (1966) FK-5


Tested by Test Id.


0

100

200

300

400

500

600

700

800

900

1000

0

5

ta

column

15

beam pc pc pc pc qc

gc

20

25

30

35

40

45




10

gb

50

A.2 – 33


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



-0.73326268E+04

-5






A.2 – 34


: :


1) 2)

lu gc pc nc

ll = cu = qb =

1.1220" 1.9685" 2.3622"

ta = cl =

II - 18

0.5906" 1.9685"

------------------------------


Grade 8.8 bolts were used. 4 and 5 bolts used either line of the cleat to column.

= 15.7480" = 3.5433" = 2.9527" = 2 X -


Remark

lp gb pb nb

U.K Fasteners: G8.8- -M20 7/8" Oversize holes Material : BS4360 Fy = -ksi Fu = -ksi

Major parameters

= 1.1220" = 2.3799" = 2.9527" = 1 X 5

B.Bose (1981) B-1

Column : 305 X 305 X 97 Beam : 457 X 191 X 67 Angle : 150 X 90 X 15

Tested by Test Id.


0

100

200

300

400

500

600

700

800

900

1000

0

2

ta

column

6

8

pc pc pc pc qc

gc

10

12

14

16

: BS4360 Experimental Polynominal M. Exponential

beam

Material : : :



4

gb

18

20

A.2 – 35


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =

© 2011 J. Ross Publishing, Inc. 0.92725157E+04

-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1963E+03 0.6159E+03 0.2325E+03 3 0.28 55.17 172.75 55.77 0.1963E+03 0.6124E+03 0.1737E+03 5 0.62 113.37 379.95 111.93 0.1519E+03 0.5969E+03 0.1619E+03 7 1.03 174.61 613.53 178.95 0.1716E+03 0.5579E+03 0.1703E+03 9 1.33 230.99 775.86 230.54 0.1863E+03 0.5136E+03 0.1693E+03 11 1.68 289.19 944.86 287.91 0.1516E+03 0.4535E+03 0.1577E+03 13 2.07 349.20 1110.74 346.36 0.1360E+03 0.3857E+03 0.1368E+03 15 2.76 424.36 1342.22 427.13 0.1003E+03 0.2907E+03 0.9812E+02 17 3.51 492.10 1531.31 487.49 0.8032E+02 0.2228E+03 0.6622E+02 19 4.04 530.47 1639.75 530.48 0.6793E+02 0.1897E+03 0.7398E+02 21 4.72 573.02 1759.11 576.03 0.6174E+02 0.1584E+03 0.5910E+02 23 5.39 617.44 1856.19 616.84 0.7323E+02 0.1366E+03 0.6577E+02 25 6.02 663.72 1937.32 656.09 0.5699E+02 0.1207E+03 0.5876E+02 27 6.63 689.10 2007.91 690.71 0.4111E+02 0.1085E+03 0.5367E+02 29 7.29 720.59 2075.94 724.75 0.5347E+02 0.9794E+02 0.4966E+02 31 8.00 758.21 2141.52 758.56 0.5068E+02 0.8882E+02 0.4662E+02 33 8.68 790.92 2199.52 789.60 0.4797E+02 0.8152E+02 0.4457E+02 --------------------------------------------------------------------------------------------------




A.2 – 36


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 19

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A


L.E.Thompson et al. (1970) A1-1 ALT


Tested by Test Id.


0

75

150

225

300

375

450

525

600

675

750

0

gb lu cu pb pb pb lp pb cl qb ll beam pc pc pc pc

18

54

72

90

gc

108 126 144 162 180

qc


36

Material : A36 Fy = 36.00 ksi (nominal) : Experimental : Polynominal : M. Exponential

ta

column

A.2 – 37


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1427E+02 0.9054E+02 0.3225E+01 3 3.43 49.00 222.73 48.94 0.1427E+02 0.3353E+02 0.1808E+02 5 6.87 98.00 298.78 103.34 0.1427E+02 0.1536E+02 0.1284E+02 7 10.30 147.00 341.07 137.27 0.1145E+02 0.1005E+02 0.7299E+01 9 20.65 175.48 413.70 178.12 0.2301E+01 0.5133E+01 0.2305E+01 11 31.35 200.10 458.72 200.86 0.2301E+01 0.3518E+01 0.2089E+01 13 42.05 223.62 491.66 222.97 0.2096E+01 0.2716E+01 0.2014E+01 15 52.75 246.04 517.94 243.37 0.2096E+01 0.2232E+01 0.1778E+01 17 63.42 260.93 539.91 260.03 0.6907E+00 0.1906E+01 0.1339E+01 19 74.06 268.28 558.87 272.55 0.6907E+00 0.1670E+01 0.1021E+01 21 84.70 275.63 575.65 281.91 0.1270E+01 0.1491E+01 0.7479E+00 23 94.80 294.00 590.01 288.41 0.9499E+01 0.1356E+01 0.5480E+00 25 97.90 330.76 594.18 342.50 0.1422E+02 0.1320E+01 0.1743E+02 27 100.20 367.50 597.20 382.55 0.1565E+02 0.1295E+01 0.1739E+02 29 102.60 404.26 600.30 424.25 0.3828E+02 0.1269E+01 0.1736E+02 31 103.40 441.00 601.31 438.14 0.4944E+02 0.1261E+01 0.1735E+02 33 104.10 477.76 602.19 450.28 0.4358E+02 0.1254E+01 0.1734E+02 35 106.00 514.50 604.56 483.21 0.1714E+02 0.1235E+01 0.1732E+02 37 108.60 551.26 607.76 528.20 0.1171E+02 0.1210E+01 0.1729E+02 39 114.90 588.00 615.13 636.95 0.5832E+01 0.1155E+01 0.1723E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.13866750E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.27629246E+03 0.15399204E+04 -0.50463775E+04 0.12162151E+05 -0.14796109E+05 Rj0 = 10.3000 58.1000 94.8000 RKj = 0.26064200E+00 -0.12358625E+00 0.16928574E+02



A.2 – 38


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 20

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

75

150

225

300

375

450

525

600

675

750

0


19

57

76

95

gc

114 133 152 171 190

qc


38


ta

column

A.2 – 39


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1267E+02 0.9054E+02 0.1216E+01 3 3.87 49.00 236.21 48.81 0.1267E+02 0.2929E+02 0.1256E+02 5 7.73 98.00 311.26 98.12 0.1267E+02 0.1353E+02 0.1281E+02 7 11.60 147.00 353.38 146.88 0.1026E+02 0.8922E+01 0.1232E+02 9 22.88 173.01 424.57 173.30 0.1901E+01 0.4673E+01 0.1872E+01 11 33.24 192.71 465.19 192.58 0.1901E+01 0.3340E+01 0.1898E+01 13 43.60 212.41 495.80 212.15 0.1455E+01 0.2632E+01 0.1839E+01 15 55.52 223.62 523.99 224.06 0.9401E+00 0.2135E+01 0.9026E+00 17 67.45 234.83 547.39 234.43 0.9401E+00 0.1808E+01 0.8775E+00 19 79.38 246.04 567.49 245.88 0.9401E+00 0.1575E+01 0.1070E+01 21 91.30 257.26 585.18 260.36 0.1301E+01 0.1400E+01 0.1365E+01 23 102.50 275.63 600.11 259.33 0.6140E+01 0.1271E+01 0.4336E-01 25 105.70 312.38 604.16 317.84 0.2042E+02 0.1238E+01 0.1832E+02 27 107.55 349.13 606.44 351.77 0.1934E+02 0.1220E+01 0.1836E+02 29 109.60 385.88 608.93 389.45 0.1671E+02 0.1201E+01 0.1840E+02 31 111.65 422.63 611.38 427.21 0.1934E+02 0.1182E+01 0.1844E+02 33 113.55 459.38 613.62 462.28 0.1935E+02 0.1166E+01 0.1848E+02 35 115.75 496.13 616.18 492.33 0.1470E+02 0.1147E+01 0.1000E+02 37 118.75 532.88 619.60 522.41 0.1050E+02 0.1123E+01 0.1005E+02 39 123.45 569.63 624.84 569.80 0.6228E+01 0.1087E+01 0.1012E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.15366583E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.10748012E+03 -0.21307681E+04 0.12642901E+05 -0.31975221E+05 0.36071279E+05 Rj0 = 0.0000 11.6000 43.6000 91.3000 102.5000 114.5000 RKj = 0.12284647E+02 -0.91816167E+01 -0.73467427E+00 -0.15979833E+01 0.18205512E+02 -0.85128330E+01



A.2 – 40


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 21

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

80

160

240

320

400

480

560

640

720

800

0


14

42

56

70

84

gc


28

qc

98

pc pc pc pc


ta

column

A.2 – 41


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3742E+02 0.9054E+02 0.2228E+02 3 1.10 41.16 96.19 41.90 0.3608E+02 0.8056E+02 0.3607E+02 5 2.20 79.38 170.30 78.50 0.3274E+02 0.5374E+02 0.3037E+02 7 4.20 128.63 245.60 129.55 0.1647E+02 0.2661E+02 0.2130E+02 9 8.30 165.37 318.64 164.19 0.6903E+01 0.1256E+02 0.6071E+01 11 14.50 202.13 376.52 202.69 0.5041E+01 0.7171E+01 0.6875E+01 13 20.40 220.50 412.31 219.23 0.2958E+01 0.5196E+01 0.3003E+01 15 27.00 238.87 442.36 238.36 0.2564E+01 0.4022E+01 0.2739E+01 17 35.00 257.26 470.93 259.18 0.2394E+01 0.3191E+01 0.2545E+01 19 42.40 275.63 492.60 278.62 0.2087E+01 0.2696E+01 0.2757E+01 21 49.60 287.88 510.72 284.32 0.1701E+01 0.2353E+01 0.9754E+00 23 57.46 297.67 528.06 293.52 0.8625E+00 0.2074E+01 0.1356E+01 25 65.98 305.02 544.70 306.47 0.8625E+00 0.1843E+01 0.1663E+01 27 74.50 312.37 559.60 321.55 0.1436E+01 0.1662E+01 0.1860E+01 29 83.50 330.76 573.85 338.88 0.5754E+02 0.1509E+01 0.1979E+01 31 84.80 367.50 575.81 364.60 0.1948E+02 0.1490E+01 0.1979E+02 33 86.50 408.11 578.33 398.25 0.2861E+02 0.1465E+01 0.1980E+02 35 89.05 447.80 582.05 448.78 0.1063E+02 0.1429E+01 0.1982E+02 37 91.10 499.07 584.97 495.52 0.1178E+03 0.1402E+01 0.8078E+02 39 91.60 532.87 585.67 535.92 0.8110E+02 0.1396E+01 0.8079E+02 41 92.00 569.63 586.23 568.23 0.9187E+02 0.1390E+01 0.8079E+02 43 92.40 606.37 586.78 600.55 0.7962E+02 0.1385E+01 0.8079E+02 45 93.00 643.13 587.62 649.02 0.6126E+02 0.1378E+01 0.8079E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.91250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.11619294E+03 0.86413062E+03 0.13989851E+03 -0.64135382E+04 0.10964574E+05 Rj0 = 0.0000 4.2000 14.5000 42.4000 83.5000 91.0000 RKj = 0.17052361E+02 -0.83067304E+01 -0.44987309E+01 -0.21426735E+01 0.17800315E+02 0.60948662E+02



A.2 – 42


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 22

0.3125" -" -"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 319.73 72.90 27 323.40 77.60 28 327.08 82.30 29 330.76 87.00 30 339.94 89.90 31 349.13 92.80 32 367.50 94.90 33 388.08 96.30 34 408.11 97.10 35 428.14 97.90 36 447.80 98.85 37 467.46 99.80 38 499.07 99.90 39 515.97 100.05 40 532.87 100.20 41 551.25 100.30 42 569.63 100.40 43 588.00 100.60 44 606.37 100.80 45 624.75 101.15 46 643.13 101.50

ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

80

160

240

320

400

480

560

640

720

800

0


16

48

64

80

96

gc

112 128 144 160

qc


32


ta

column

A.2 – 43


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.99583333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.50780109E+03 0.63517255E+04 -0.26791101E+05 0.55681030E+05 -0.55424116E+05 Rj0 = 0.0000 4.7000 14.2000 32.8000 92.8000 99.8000 RKj = 0.65524552E+01 0.33845655E+01 -0.80469602E+01 -0.19560629E+01 0.21284012E+02 0.89466331E+02



A.2 – 44


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 23

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

85

170

255

340

425

510

595

680

765

850

0


17

51

68

85

gc

102 119 136 153 170

qc


34


ta

column

A.2 – 45


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4932E+02 0.9054E+02 0.6148E+02 3 0.90 44.39 79.70 47.24 0.4835E+02 0.8419E+02 0.4435E+02 5 2.80 110.26 198.83 107.75 0.2144E+02 0.4213E+02 0.2193E+02 7 5.90 147.00 282.66 149.33 0.8667E+01 0.1814E+02 0.7905E+01 9 12.70 183.76 362.74 183.83 0.4100E+01 0.8159E+01 0.4104E+01 11 20.70 211.31 413.86 211.58 0.2784E+01 0.5126E+01 0.2741E+01 13 28.30 229.69 447.49 230.55 0.2136E+01 0.3855E+01 0.2320E+01 15 36.65 248.06 476.09 248.38 0.2270E+01 0.3064E+01 0.2042E+01 17 45.00 266.81 499.43 265.25 0.2221E+01 0.2560E+01 0.1997E+01 19 54.00 280.58 520.70 282.70 0.8987E+00 0.2187E+01 0.1861E+01 21 62.85 296.75 538.82 298.24 0.2879E+01 0.1921E+01 0.1647E+01 23 70.15 313.85 552.30 309.61 0.1634E+01 0.1748E+01 0.1470E+01 25 78.33 321.94 565.83 320.93 0.5851E+00 0.1593E+01 0.1307E+01 27 88.38 327.82 581.03 333.31 0.5851E+00 0.1439E+01 0.1169E+01 29 96.85 343.25 592.83 342.88 0.3621E+01 0.1332E+01 0.1096E+01 31 102.00 383.66 599.49 384.03 0.1903E+02 0.1276E+01 0.2199E+02 33 104.20 429.24 602.29 432.40 0.6616E+02 0.1253E+01 0.2198E+02 35 104.80 480.32 603.04 483.73 0.9006E+02 0.1247E+01 0.8554E+02 37 105.20 517.81 603.54 517.94 0.9738E+02 0.1243E+01 0.8554E+02 39 105.55 554.19 603.97 547.88 0.1127E+03 0.1240E+01 0.8554E+02 41 105.95 588.73 604.47 582.09 0.7056E+02 0.1236E+01 0.8553E+02 43 106.60 635.77 605.27 637.69 0.7023E+02 0.1229E+01 0.8553E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10050000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.31272088E+02 0.19965538E+04 -0.96974738E+04 0.21391855E+05 -0.21792129E+05 Rj0 = 0.0000 4.0000 8.4000 24.0000 100.3000 104.2000 RKj = 0.70485870E-02 0.11076194E+00 0.30486987E+00 0.57329150E+00 0.20926854E+02 0.63557721E+02



A.2 – 46


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 24

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

85

170

255

340

425

510

595

680

765

850

0


17

51

68

85

gc

102 119 136 153 170

qc


34


ta

column

A.2 – 47


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.5548E+02 0.9054E+02 0.6033E+02 3 0.80 44.39 71.21 43.19 0.4962E+02 0.8567E+02 0.4550E+02 5 3.10 110.26 210.80 110.56 0.1871E+02 0.3766E+02 0.1760E+02 7 6.40 147.00 291.33 146.87 0.7961E+01 0.1658E+02 0.7237E+01 9 14.60 183.76 377.22 183.76 0.3569E+01 0.7125E+01 0.3653E+01 11 23.20 211.31 426.02 211.58 0.2625E+01 0.4616E+01 0.2579E+01 13 31.10 229.69 457.83 229.96 0.2088E+01 0.3543E+01 0.2158E+01 15 39.65 248.06 484.97 248.01 0.2215E+01 0.2859E+01 0.2097E+01 17 48.35 266.81 507.74 266.22 0.2099E+01 0.2406E+01 0.2080E+01 19 57.25 280.58 527.63 281.00 0.9710E+00 0.2080E+01 0.1210E+01 21 66.88 290.78 546.34 291.92 0.1132E+01 0.1822E+01 0.1058E+01 23 77.42 302.73 564.39 302.27 0.1132E+01 0.1609E+01 0.9115E+00 25 87.65 313.85 579.99 311.06 0.1040E+01 0.1449E+01 0.8138E+00 27 95.60 330.76 591.14 336.39 0.4207E+01 0.1346E+01 0.7121E+01 29 102.60 383.66 600.26 386.13 0.2611E+02 0.1269E+01 0.7093E+01 31 104.10 429.24 602.15 472.65 0.1369E+03 0.1254E+01 0.5768E+02 33 104.45 480.32 602.59 492.83 0.1201E+03 0.1251E+01 0.5767E+02 35 104.75 517.81 602.97 510.14 0.1298E+03 0.1248E+01 0.5767E+02 37 105.05 554.19 603.34 527.44 0.1127E+03 0.1245E+01 0.5767E+02 39 105.45 588.73 603.84 550.51 0.7056E+02 0.1241E+01 0.5767E+02 41 106.60 635.77 605.26 616.83 0.2766E+02 0.1229E+01 0.5767E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10050000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.19410764E+02 0.14923016E+04 -0.71067588E+04 0.15241550E+05 -0.15263434E+05 Rj0 = 0.0000 4.4000 9.4000 19.7000 52.9000 92.6000 102.6000 RKj = 0.31096754E+01 0.11699326E+01 -0.22788616E+01 -0.53809066E+00 -0.77114484E+00 0.63553186E+01 0.50586562E+02



A.2 – 48


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 25

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A


L.E.Thompson et al. (1970) B1-1 ALT


Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


16

48

64

80

96

gc

112 128 144 160

qc


32


ta

column

A.2 – 49


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.94583333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.57706361E+03 -0.78942103E+04 0.39226983E+05 -0.81152949E+05 0.77092146E+05 Rj0 = 6.5000 21.2000 79.6000 92.5000 RKj = 0.13247002E+02 -0.10043723E+02 0.26144943E+02 -0.14838231E+02



A.2 – 50


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 26

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


18

54

72

90

gc

108 126 144 162 180

qc


36


ta

column

A.2 – 51


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10750000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.59013481E+03 -0.11809278E+04 -0.43164459E+04 0.19869415E+05 -0.23645803E+05 Rj0 = 0.0000 13.7000 19.3000 44.5000 68.1000 91.0000 96.6000 100.0000 RKj = -0.30940337E+01 0.39469528E+01 0.16735861E+01 -0.69819829E+00 -0.10885376E+01 0.80142414E+01 0.26254975E+01 0.11610873E+02



A.2 – 52


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 27

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

23

ta

column

69

beam pc pc pc pc qc

gc

92

115 138 161 184 207 230




46

gb

A.2 – 53


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.13358333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.41709333E+03 0.32570617E+04 -0.31328362E+05 0.93621778E+05 -0.11527189E+06 Rj0 = 0.0000 5.0000 77.4000 91.9000 112.0000 RKj = 0.37647976E+01 -0.87339727E+01 0.29132991E+02 -0.14785694E+02 -0.72835694E+01



A.2 – 54


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 28

0.5000" -" -"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 464.23 260.70 27 481.72 275.40 28 499.21 290.10 29 516.71 304.80 30 553.09 306.10 31 590.39 307.50 32 627.70 308.90 33 664.07 310.10 34 700.45 311.30 35 737.20 312.70 36 773.95 314.10 37 809.97 315.60 38 845.99 317.10 39 882.37 319.85 40 918.76 322.60 41 955.51 324.90 42 992.26 327.20 43 1029.01 330.70 44 1065.76 334.20 45 1102.51 340.85 46 1139.26 347.50 47 1176.00 357.60

ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A.




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


54

qc

gc


108 162 216 270 324 378 432 486 540


ta

column

A.2 – 55


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1208E+03 0.2120E+03 0.1842E+02 3 0.70 84.53 146.51 92.66 0.1026E+03 0.2035E+03 0.1304E+03 5 1.60 155.82 312.88 143.24 0.6525E+02 0.1608E+03 0.5424E+02 7 3.20 222.71 502.15 225.76 0.3451E+02 0.8510E+02 0.4934E+02 9 9.20 234.60 771.11 236.21 0.1994E+01 0.2642E+02 0.5412E+00 11 27.00 260.18 1035.72 258.22 0.9525E+00 0.9416E+01 0.6687E+00 13 49.00 277.09 1192.52 277.66 0.8745E+00 0.5566E+01 0.4097E-01 15 84.20 313.85 1346.10 311.37 0.1044E+01 0.3508E+01 0.1518E+01 17 119.40 350.60 1452.18 357.75 0.1044E+01 0.2619E+01 0.9329E+00 19 152.72 379.02 1530.75 377.60 0.6391E+00 0.2135E+01 0.3821E+00 21 184.15 399.11 1592.77 391.50 0.6391E+00 0.1829E+01 0.5728E+00 23 215.58 419.20 1646.60 415.81 0.6391E+00 0.1607E+01 0.9809E+00 25 246.00 446.73 1692.86 451.25 0.1190E+01 0.1442E+01 0.1333E+01 27 275.40 481.72 1733.31 494.14 0.1190E+01 0.1314E+01 0.1568E+01 29 304.80 516.71 1770.37 542.54 0.2581E+02 0.1210E+01 0.1712E+01 31 307.50 590.39 1773.63 600.96 0.2664E+02 0.1201E+01 0.2164E+02 33 310.10 664.07 1776.75 657.24 0.3031E+02 0.1193E+01 0.2165E+02 35 312.70 737.20 1779.84 713.54 0.2625E+02 0.1185E+01 0.2166E+02 37 315.60 809.97 1783.27 776.37 0.2401E+02 0.1176E+01 0.2167E+02 39 319.85 882.37 1788.26 868.48 0.1323E+02 0.1163E+01 0.2168E+02 41 324.90 955.51 1794.11 978.00 0.1598E+02 0.1148E+01 0.2169E+02 43 330.70 1029.01 1800.75 1045.62 0.1050E+02 0.1132E+01 0.5066E+01 45 340.85 1102.51 1812.17 1097.15 0.5526E+01 0.1104E+01 0.5086E+01 47 357.60 1176.00 1830.49 1182.56 0.3638E+01 0.1061E+01 0.5111E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.30675000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.10264832E+04 -0.13648205E+05 0.66734672E+05 -0.14599267E+06 0.14641175E+06 Rj0 = 0.0000 0.7000 3.2000 27.0000 49.0000 137.0000 304.8000 327.2000 RKj = 0.11605567E+03 -0.72069868E+02 -0.44166934E+02 0.18631459E+01 0.29660457E+00 -0.97343272E-01 0.19920503E+02 -0.16639962E+02



A.2 – 56


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 29

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

75

150

225

300

375

450

525

600

675

750

0

13

ta

column

39

beam pc pc pc pc qc

gc

52

65

78

91

104 117 130




26

gb

A.2 – 57


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.73083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.14051820E+03 0.16923399E+04 -0.12317928E+05 0.30693851E+05 -0.31092260E+05 Rj0 = 11.0000 18.3000 48.1000 72.1000 78.8000 RKj = 0.52588977E+01 -0.28722734E+01 -0.23213804E+01 0.36489949E+01 0.16139291E+02



A.2 – 58


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 30

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

75

150

225

300

375

450

525

600

675

750

0

18

ta

column

54

beam pc pc pc pc qc

gc

72

90

108 126 144 162 180




36

gb

A.2 – 59


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.99500000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.45908760E+03 -0.74168500E+03 -0.37372130E+04 0.14186913E+05 -0.15463007E+05 Rj0 = 15.4000 22.6000 39.5000 46.4000 102.1000 109.5000 RKj = 0.41137346E+01 -0.22971675E+01 0.31992936E+01 -0.47344042E+01 0.31404400E+01 0.10951706E+02



A.2 – 60


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 31

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A


L.E.Thompson et al. (1970) D1-1 ALT


Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


14

42

56

70

84

gc


28

qc

98

pc pc pc pc


ta

column

A.2 – 61


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5





A.2 – 62


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 32

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


15

45

60

75

90

gc

105 120 135 150

qc


30


ta

column

A.2 – 63


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5





A.2 – 64


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 33

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


14

42

56

70

84

gc


28

qc

98

pc pc pc pc


ta

column

A.2 – 65


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7596E+02 0.9496E+02 0.8097E+02 3 1.10 80.86 100.90 77.35 0.6303E+02 0.8451E+02 0.6018E+02 5 2.70 150.31 204.05 153.88 0.3376E+02 0.4596E+02 0.3700E+02 7 5.40 221.23 286.50 220.89 0.1951E+02 0.2100E+02 0.1570E+02 9 10.90 276.36 363.97 277.09 0.7056E+01 0.9953E+01 0.8619E+01 11 16.65 313.11 410.08 315.80 0.5880E+01 0.6590E+01 0.5358E+01 13 24.05 349.86 450.91 350.01 0.4251E+01 0.4685E+01 0.4347E+01 15 32.38 370.22 484.90 367.85 0.6505E+00 0.3586E+01 0.9303E-01 17 40.74 375.66 511.92 372.68 0.6505E+00 0.2929E+01 0.9624E+00 19 49.10 381.10 534.47 382.06 0.6505E+00 0.2490E+01 0.1186E+01 21 57.46 386.53 553.90 391.40 0.6505E+00 0.2175E+01 0.1010E+01 23 65.82 391.97 571.04 398.66 0.6505E+00 0.1937E+01 0.7269E+00 25 71.10 422.63 580.95 430.43 0.2532E+02 0.1814E+01 0.2636E+02 27 73.40 480.68 585.09 490.99 0.2833E+02 0.1765E+01 0.2630E+02 29 75.80 556.39 589.30 554.03 0.3047E+02 0.1717E+01 0.2624E+02 31 78.20 626.95 593.39 616.93 0.2994E+02 0.1672E+01 0.2619E+02 33 80.60 700.09 597.38 679.72 0.2862E+02 0.1630E+01 0.2614E+02 35 83.30 771.76 601.61 750.23 0.2371E+02 0.1586E+01 0.2609E+02 37 87.00 845.09 607.42 846.68 0.1894E+02 0.1529E+01 0.2604E+02 39 91.10 918.76 613.63 953.36 0.1797E+02 0.1470E+01 0.2600E+02 --------------------------------------------------------------------------------------------------




A.2 – 66


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 34

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


15

45

60

75

90

gc

105 120 135 150

qc


30


ta

column

A.2 – 67


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5





A.2 – 68


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 35

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


15

45

60

75

90

gc

105 120 135 150

qc


30


ta

column

A.2 – 69


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.94083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.33225987E+03 -0.23049668E+04 0.96618643E+04 -0.19865358E+05 0.20424157E+05 Rj0 = 12.5000 24.8000 44.6000 78.2000 RKj = 0.11063111E+01 0.38458198E+01 -0.25508858E+01 0.25057791E+02



A.2 – 70


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 36

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


14

42

56

70

84

gc


28

qc

98

pc pc pc pc


ta

column

A.2 – 71


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7350E+02 0.9496E+02 0.7266E+02 3 1.30 80.86 117.38 82.54 0.5145E+02 0.7989E+02 0.5358E+02 5 2.90 150.67 212.89 150.00 0.3309E+02 0.4254E+02 0.3199E+02 7 7.10 221.96 317.11 224.84 0.1201E+02 0.1554E+02 0.1033E+02 9 14.00 275.63 391.09 272.37 0.3295E+01 0.7783E+01 0.4049E+01 11 23.10 284.81 446.39 287.62 0.1009E+01 0.4860E+01 0.2150E+00 13 32.20 294.00 484.26 294.43 0.2171E+01 0.3603E+01 0.1761E+01 15 38.40 312.37 504.89 309.71 0.3618E+01 0.3085E+01 0.3032E+01 17 45.85 337.73 526.13 334.08 0.2083E+01 0.2642E+01 0.3276E+01 19 53.40 350.41 544.79 356.07 0.1356E+01 0.2316E+01 0.2428E+01 21 61.80 361.80 563.05 370.78 0.1356E+01 0.2044E+01 0.1061E+01 23 68.60 376.69 576.42 374.44 0.3533E+01 0.1869E+01 0.4893E-01 25 73.40 407.93 585.10 435.16 0.2395E+02 0.1765E+01 0.2762E+02 27 75.80 483.64 589.31 501.14 0.3356E+02 0.1717E+01 0.2737E+02 29 77.80 554.10 592.73 555.68 0.3583E+02 0.1680E+01 0.2718E+02 31 79.80 626.95 596.07 609.88 0.3435E+02 0.1644E+01 0.2702E+02 33 82.10 700.45 599.82 671.82 0.2903E+02 0.1605E+01 0.2685E+02 35 84.90 771.76 604.14 746.73 0.2373E+02 0.1561E+01 0.2667E+02 37 88.30 845.26 609.41 837.09 0.1882E+02 0.1510E+01 0.2649E+02 39 93.30 918.76 616.73 969.00 0.1470E+02 0.1442E+01 0.2629E+02 --------------------------------------------------------------------------------------------------




A.2 – 72


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 37

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A


L.E.Thompson et al. (1970) E1-1 ALT


Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0


16

48

64

80

96

gc

112 128 144 160

qc


32


ta

column

A.2 – 73


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1782E+03 0.2223E+03 0.1786E+03 3 0.40 71.29 88.59 65.80 0.1545E+03 0.2197E+03 0.1510E+03 5 1.00 142.60 216.20 145.46 0.1093E+03 0.2026E+03 0.1157E+03 7 1.70 211.31 344.71 214.49 0.8952E+02 0.1623E+03 0.8289E+02 9 3.00 298.42 508.21 292.60 0.5145E+02 0.9595E+02 0.4088E+02 11 5.30 334.24 665.81 340.98 0.1340E+01 0.5020E+02 0.7176E+01 13 10.80 337.58 849.64 337.03 0.1351E+01 0.2354E+02 -0.1109E+01 15 16.40 349.13 956.20 345.03 0.3275E+01 0.1566E+02 0.3175E+01 17 23.90 385.87 1054.06 392.70 0.5376E+01 0.1103E+02 0.5649E+01 19 33.45 437.32 1144.16 436.16 0.4742E+01 0.8156E+01 0.3772E+01 21 41.45 468.56 1203.40 464.90 0.2744E+01 0.6754E+01 0.3554E+01 23 49.38 479.77 1252.94 480.59 0.4413E+00 0.5802E+01 0.8804E+00 25 58.52 483.81 1302.23 489.98 0.4413E+00 0.5013E+01 0.1151E+01 27 67.10 514.50 1342.74 500.52 0.6515E+00 0.4461E+01 0.1291E+01 29 68.00 540.96 1346.75 546.09 0.5320E+02 0.4410E+01 0.5063E+02 31 70.30 664.81 1356.82 662.57 0.5388E+02 0.4287E+01 0.5065E+02 33 72.10 761.83 1364.49 753.75 0.5390E+02 0.4195E+01 0.5066E+02 35 74.55 873.73 1374.70 877.90 0.4090E+02 0.4077E+01 0.5068E+02 37 78.05 992.25 1388.51 996.36 0.2827E+02 0.3924E+01 0.2047E+02 39 83.20 1109.11 1408.46 1101.80 0.1884E+02 0.3715E+01 0.2048E+02 41 86.80 1176.00 1421.38 1175.52 0.1696E+02 0.3587E+01 0.2048E+02 43 92.90 1249.50 1442.59 1248.56 0.8209E+01 0.3388E+01 0.6066E+01 45 98.40 1286.26 1461.00 1281.93 0.5951E+01 0.3227E+01 0.6066E+01 47 105.80 1323.00 1484.12 1326.81 0.4965E+01 0.3037E+01 0.6064E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.93166667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.12130037E+03 0.46342497E+04 -0.14344499E+05 0.19390732E+05 -0.11753405E+05 Rj0 = 3.8000 16.4000 44.8000 67.1000 76.1000 89.3000 RKj = 0.10705203E+01 0.32061988E+01 -0.29104256E+01 0.49332602E+02 -0.30222866E+02 -0.14416609E+02



A.2 – 74


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 38

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0


21

63

84

gc

105 126 147 168 189 210

qc


42


ta

column

A.2 – 75


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1782E+03 0.2223E+03 0.1691E+03 3 0.40 71.29 88.59 62.73 0.1545E+03 0.2197E+03 0.1451E+03 5 1.00 142.60 216.20 140.39 0.1093E+03 0.2026E+03 0.1148E+03 7 1.70 211.31 344.71 210.57 0.8569E+02 0.1623E+03 0.8686E+02 9 3.10 298.42 517.64 303.03 0.5406E+02 0.9251E+02 0.4859E+02 11 4.30 349.13 609.41 348.56 0.3182E+02 0.6367E+02 0.2889E+02 13 12.30 400.57 882.70 404.83 0.2227E+01 0.2068E+02 0.1134E+01 15 23.35 437.32 1047.96 439.42 0.4955E+01 0.1127E+02 0.5247E+01 17 34.50 477.76 1152.65 476.52 0.2019E+01 0.7935E+01 0.2154E+01 19 45.10 500.17 1227.16 500.15 0.2986E+01 0.6276E+01 0.2627E+01 21 55.63 514.50 1287.42 512.21 0.1492E-14 0.5235E+01 -0.4086E-01 23 67.10 514.50 1342.74 516.28 0.3762E+00 0.4461E+01 0.6333E+00 25 80.22 525.08 1396.93 525.82 0.8067E+00 0.3834E+01 0.7422E+00 27 93.34 535.67 1444.08 534.66 0.8067E+00 0.3375E+01 0.5910E+00 29 101.35 602.89 1470.21 603.84 0.4271E+02 0.3150E+01 0.4522E+02 31 103.80 713.32 1477.89 714.60 0.4851E+02 0.3087E+01 0.4519E+02 33 105.80 810.34 1484.04 804.97 0.4509E+02 0.3038E+01 0.4517E+02 35 109.00 937.13 1493.70 949.46 0.3384E+02 0.2963E+01 0.4514E+02 37 113.20 1047.37 1506.05 1034.91 0.2316E+02 0.2870E+01 0.2033E+02 39 118.30 1142.56 1520.21 1138.47 0.1967E+02 0.2768E+01 0.2029E+02 41 122.60 1212.76 1532.03 1225.65 0.1240E+02 0.2686E+01 0.2026E+02 43 130.70 1286.26 1553.10 1281.41 0.7289E+01 0.2548E+01 0.6866E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.11925000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.50153364E+02 0.61228711E+04 -0.30064977E+05 0.61162931E+05 -0.55180581E+05 Rj0 = 6.5000 18.9000 49.9000 99.9000 109.0000 122.6000 RKj = -0.26679000E+01 0.66849581E+01 -0.38180954E+01 0.44736399E+02 -0.24775393E+02 -0.13358764E+02



A.2 – 76


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 39

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

23

ta

column

69

beam pc pc pc pc qc

gc

92

115 138 161 184 207 230




46

gb

A.2 – 77


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1445E+03 0.2223E+03 0.3050E+02 3 0.60 86.72 132.19 86.76 0.1451E+03 0.2160E+03 0.1407E+03 5 1.10 159.49 236.23 155.73 0.1295E+03 0.1979E+03 0.1353E+03 7 5.60 206.53 680.46 208.30 0.3326E+01 0.4719E+02 -0.4549E+00 9 13.80 240.71 912.00 245.59 0.5053E+01 0.1848E+02 0.9214E+01 11 19.10 330.76 995.46 297.62 0.4523E+02 0.1357E+02 0.9549E+01 13 30.60 367.50 1120.00 377.09 0.4704E+01 0.8828E+01 0.4402E+01 15 39.20 404.26 1187.84 407.29 0.4477E+01 0.7092E+01 0.3031E+01 17 52.80 459.37 1272.25 449.52 0.2139E+01 0.5476E+01 0.3263E+01 19 62.90 477.76 1323.49 479.00 0.1391E+01 0.4713E+01 0.2456E+01 21 74.20 488.05 1373.08 501.86 0.9106E+00 0.4096E+01 0.1511E+01 23 85.50 498.34 1416.63 512.41 0.3249E+02 0.3633E+01 0.3597E+00 25 87.90 592.42 1425.30 611.18 0.4760E+02 0.3549E+01 0.4104E+02 27 89.30 665.92 1430.25 668.54 0.5270E+02 0.3502E+01 0.4091E+02 29 92.00 809.23 1439.65 778.67 0.4831E+02 0.3415E+01 0.4067E+02 31 93.60 882.00 1445.09 843.64 0.4193E+02 0.3366E+01 0.4053E+02 33 96.70 988.57 1455.46 968.91 0.3675E+02 0.3275E+01 0.4029E+02 35 99.50 1065.75 1464.58 1081.42 0.2162E+02 0.3197E+01 0.4008E+02 37 103.10 1139.25 1475.66 1168.17 0.1934E+02 0.3105E+01 0.9784E+01 39 107.95 1212.75 1490.58 1214.93 0.1246E+02 0.2987E+01 0.9508E+01 41 114.50 1286.26 1509.52 1276.18 0.9077E+01 0.2845E+01 0.9209E+01 43 122.80 1350.76 1532.45 1351.40 0.7843E+01 0.2683E+01 0.8932E+01 45 133.20 1433.26 1559.42 1443.01 0.6890E+01 0.2508E+01 0.8705E+01 47 147.00 1451.63 1592.63 1460.42 -0.2552E+01 0.2311E+01 0.1188E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.13000000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = -0.13097285E+03 0.73837308E+04 -0.46819402E+05 0.11513534E+06 -0.12484823E+06 Rj0 = 0.0000 1.4000 17.8000 57.8500 85.5000 101.2000 133.2000 RKj = 0.11823233E+03 -0.12003844E+03 -0.92111515E-01 -0.56202712E+00 0.40912007E+02 -0.30061901E+02 -0.73506487E+01



A.2 – 78


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 40

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

22

ta

column

66

beam pc pc pc pc qc

gc

88

110 132 154 176 198 220




44

gb

A.2 – 79


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1239E+03 0.2223E+03 0.7746E+02 3 0.70 86.72 153.67 87.10 0.1225E+03 0.2135E+03 0.1128E+03 5 1.30 159.49 274.75 150.09 0.1006E+03 0.1871E+03 0.9798E+02 7 3.80 198.77 575.24 207.26 0.3103E+01 0.7338E+02 -0.6592E+00 9 10.80 220.50 849.64 218.12 0.4558E+01 0.2354E+02 0.6642E+01 11 23.30 312.37 1047.34 308.47 0.5438E+01 0.1129E+02 0.5340E+01 13 35.10 367.50 1157.36 364.42 0.4958E+01 0.7815E+01 0.4964E+01 15 45.70 422.63 1230.91 420.68 0.5521E+01 0.6204E+01 0.5286E+01 17 55.05 446.10 1284.35 452.77 0.8571E+00 0.5283E+01 0.1703E+01 19 63.00 459.37 1324.09 455.68 0.5903E+01 0.4705E+01 -0.1078E+01 21 66.50 498.34 1340.06 502.65 0.2407E+02 0.4495E+01 0.4183E+02 23 69.40 592.42 1352.97 622.31 0.5736E+02 0.4333E+01 0.4070E+02 25 70.50 665.92 1357.72 666.85 0.5969E+02 0.4276E+01 0.4028E+02 27 72.00 740.88 1364.11 726.84 0.4851E+02 0.4200E+01 0.3971E+02 29 74.60 845.62 1374.94 828.82 0.3308E+02 0.4074E+01 0.3875E+02 31 77.37 931.00 1385.82 934.67 0.2940E+02 0.3953E+01 0.3777E+02 33 80.70 1029.00 1398.88 1031.77 0.2484E+02 0.3814E+01 0.1742E+02 35 86.50 1127.00 1420.25 1127.76 0.1690E+02 0.3598E+01 0.1573E+02 37 93.55 1212.75 1444.78 1214.71 0.8855E+01 0.3369E+01 0.9769E+01 39 101.40 1286.26 1470.34 1285.62 0.9171E+01 0.3149E+01 0.8373E+01 41 109.10 1350.76 1493.85 1346.11 0.7621E+01 0.2962E+01 0.7394E+01 43 122.10 1433.26 1530.57 1434.89 0.6400E+01 0.2696E+01 0.6373E+01 45 134.15 1460.81 1561.80 1461.45 -0.1447E+01 0.2493E+01 -0.1513E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12583333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.33282284E+03 0.50544825E+04 -0.52687471E+05 0.16617462E+06 -0.21281962E+06 Rj0 = 1.8000 49.1000 65.3000 79.3000 89.4000 127.8000 0.0000 RKj = -0.73805566E+02 -0.16779921E+01 0.44259993E+02 -0.19255481E+02 -0.42915337E+01 -0.73913835E+01 0.60141738E+02



A.2 – 80


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 41

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

18

ta

column

54

beam pc pc pc pc qc

gc

72

90

108 126 144 162 180




36

gb

A.2 – 81


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10625000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.47627138E+03 0.79562123E+03 -0.72281906E+04 0.21830806E+05 -0.28036302E+05 Rj0 = 50.7000 65.3000 79.0000 99.1000 RKj = 0.10414642E+01 0.38485581E+02 -0.28421809E+02 -0.56531269E+01



A.2 – 82


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 42

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

18

ta

column

54

beam pc pc pc pc qc

gc

72

90

108 126 144 162 180




36

gb

A.2 – 83


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10366667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.37257876E+03 0.20564792E+04 -0.12530905E+05 0.30776580E+05 -0.34794350E+05 Rj0 = 65.8000 75.9000 89.9000 RKj = 0.48428510E+02 -0.30773009E+02 -0.10948301E+02



A.2 – 84


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 43

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


31

93

gc

124 155 186 217 248 279 310

qc


62


ta

column

A.2 – 85


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3608E+02 0.9054E+02 0.5041E+02 3 3.70 73.50 231.23 73.33 0.9831E+01 0.3080E+02 0.3832E+01 5 13.90 110.26 372.11 108.08 0.3239E+01 0.7471E+01 0.3360E+01 7 27.20 147.00 443.24 147.64 0.2867E+01 0.3993E+01 0.2558E+01 9 39.60 183.76 484.83 186.12 0.2566E+01 0.2862E+01 0.3909E+01 11 54.80 215.35 522.44 211.61 0.1604E+01 0.2160E+01 0.2038E+01 13 69.60 232.26 551.22 236.66 0.1117E+01 0.1761E+01 0.1131E+01 15 84.40 248.43 575.20 242.70 0.1092E+01 0.1496E+01 -0.2921E+00 17 93.90 291.98 588.81 294.01 0.1689E+02 0.1367E+01 0.2035E+02 19 97.60 366.95 593.83 368.89 0.2469E+02 0.1323E+01 0.2013E+02 21 102.80 457.17 600.49 472.92 0.1409E+02 0.1267E+01 0.1989E+02 23 113.30 553.01 613.27 542.19 0.5822E+01 0.1169E+01 0.5940E+01 25 127.40 624.76 628.95 624.65 0.5562E+01 0.1060E+01 0.5797E+01 27 139.70 698.26 641.49 695.99 0.5601E+01 0.9817E+00 0.5815E+01 29 153.30 768.80 654.33 775.58 0.5644E+01 0.9089E+00 0.5895E+01 31 165.90 845.26 665.41 850.39 0.6465E+01 0.8515E+00 0.5979E+01 33 176.70 918.76 674.49 915.32 0.6483E+01 0.8077E+00 0.6044E+01 35 188.70 992.26 683.87 988.22 0.5899E+01 0.7654E+00 0.6103E+01 37 201.70 1065.76 693.49 1067.87 0.5654E+01 0.7248E+00 0.6150E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.19558333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.10312842E+04 -0.10838972E+05 0.49060105E+05 -0.98558393E+05 0.88381059E+05 Rj0 = 0.0000 3.7000 39.6000 91.2000 103.2000 RKj = -0.36397225E+01 0.51471853E+01 -0.29898281E+01 0.21360944E+02 -0.13635890E+02



A.2 – 86


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 44

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

30

ta

column

90

beam pc pc pc pc qc

gc

120 150 180 210 240 270 300




60

gb

A.2 – 87


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.19983333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.54364181E+03 -0.42372141E+04 0.14806640E+05 -0.23829531E+05 0.15272050E+05 Rj0 = 0.0000 3.4000 59.9000 83.9000 93.8000 RKj = 0.55967636E+01 -0.87423765E+01 0.46560963E+00 0.25003926E+02 -0.16827610E+02



A.2 – 88


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 45

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

31

ta

column

93

beam pc pc pc pc qc

gc

124 155 186 217 248 279 310




62

gb

A.2 – 89


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5





A.2 – 90


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 46

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

30

ta

column

90

beam pc pc pc pc qc

gc

120 150 180 210 240 270 300




60

gb

A.2 – 91


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18933333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.13195329E+04 -0.21710605E+05 0.11048185E+06 -0.23128417E+06 0.20969660E+06 Rj0 = 0.0000 3.6000 18.5000 34.8000 50.3000 71.8000 78.9000 80.2000 RKj = 0.13415349E+02 -0.21797779E+02 0.27872844E+01 -0.32487291E+01 -0.40766691E+00 0.20877948E+02 0.40549235E+02 -0.46359387E+02



A.2 – 92


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 47

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0


30

90

gc

120 150 180 210 240 270 300

qc


60


ta

column

A.2 – 93


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2042E+02 0.9054E+02 0.2247E+02 3 4.20 74.96 245.52 74.57 0.1301E+02 0.2664E+02 0.1234E+02 5 16.55 128.26 390.31 129.61 0.2483E+01 0.6319E+01 0.1702E+01 7 32.35 162.80 462.26 164.42 0.1916E+01 0.3419E+01 0.2343E+01 9 45.65 188.53 501.09 188.63 0.1965E+01 0.2529E+01 0.1309E+01 11 58.00 205.07 529.18 202.76 0.9058E+00 0.2057E+01 0.1166E+01 13 74.33 227.85 559.33 228.91 0.1790E+01 0.1665E+01 0.2140E+01 15 92.40 260.20 586.72 277.80 0.2075E+02 0.1386E+01 0.3169E+01 17 95.47 333.69 590.94 333.91 0.2397E+02 0.1348E+01 0.1835E+02 19 98.55 406.82 595.07 390.61 0.2347E+02 0.1313E+01 0.1843E+02 21 102.77 479.22 600.56 468.48 0.1351E+02 0.1267E+01 0.1850E+02 23 108.10 551.26 607.11 567.32 0.1128E+02 0.1215E+01 0.1855E+02 25 124.70 623.28 626.06 628.53 0.5003E+01 0.1079E+01 0.3602E+01 27 138.10 697.51 639.91 695.61 0.5910E+01 0.9911E+00 0.6754E+01 29 150.00 771.76 651.30 774.57 0.6473E+01 0.9255E+00 0.6517E+01 31 161.20 846.72 661.36 846.39 0.6591E+01 0.8719E+00 0.6313E+01 33 172.30 918.76 670.91 915.48 0.6069E+01 0.8247E+00 0.6142E+01 35 185.50 992.26 681.42 995.45 0.6048E+01 0.7762E+00 0.5982E+01 37 195.80 1058.40 689.16 1056.56 0.6422E+01 0.7427E+00 0.5888E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20816667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.43613438E+03 0.88133715E+04 -0.46666593E+05 0.10651642E+06 -0.10847300E+06 Rj0 = 9.0000 92.4000 108.1000 132.1000 RKj = 0.19913544E+01 0.15072655E+02 -0.14831416E+02 0.33959388E+01



A.2 – 94


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 48

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

32

ta

column

96

beam pc pc pc pc qc

gc

128 160 192 224 256 288 320




64

gb

A.2 – 95


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1750E+02 0.9054E+02 0.1421E+02 3 4.90 74.96 262.57 75.51 0.1055E+02 0.2234E+02 0.1340E+02 5 19.80 109.51 409.15 116.78 0.2850E+01 0.5342E+01 0.3455E+01 7 31.30 147.00 458.55 142.60 0.2787E+01 0.3523E+01 0.1582E+01 9 45.70 178.61 501.22 172.05 0.1906E+01 0.2526E+01 0.2684E+01 11 57.60 198.46 528.35 205.70 0.1293E+01 0.2069E+01 0.2660E+01 13 76.70 211.68 563.22 230.27 0.1117E+02 0.1622E+01 -0.4909E+00 15 82.70 298.42 572.64 312.61 0.2024E+02 0.1522E+01 0.1311E+02 17 85.80 370.44 577.32 352.28 0.2087E+02 0.1475E+01 0.1249E+02 19 89.90 443.21 583.30 401.88 0.1468E+02 0.1417E+01 0.1172E+02 21 99.63 515.24 596.43 508.08 0.7401E+01 0.1301E+01 0.1018E+02 23 112.55 587.27 612.39 603.63 0.4474E+01 0.1175E+01 0.5552E+01 25 127.80 660.40 629.37 681.68 0.5155E+01 0.1057E+01 0.4815E+01 27 141.75 734.63 643.63 747.44 0.5500E+01 0.9691E+00 0.4674E+01 29 154.85 809.24 655.84 809.23 0.5903E+01 0.9009E+00 0.4784E+01 31 166.70 882.74 666.16 866.96 0.6549E+01 0.8478E+00 0.4967E+01 33 179.70 955.51 676.78 932.96 0.4900E+01 0.7971E+00 0.5186E+01 35 194.30 1014.30 688.05 1010.35 0.3105E+01 0.7475E+00 0.5408E+01 37 208.50 1058.40 698.35 1088.41 0.3105E+01 0.7053E+00 0.5580E+01 --------------------------------------------------------------------------------------------------




A.2 – 96


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 49

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

31

ta

column

93

beam pc pc pc pc qc

gc

124 155 186 217 248 279 310




62

gb

A.2 – 97


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6405E+02 0.9496E+02 0.5341E+02 3 1.80 77.92 154.02 66.16 0.1956E+02 0.6660E+02 0.2304E+02 5 5.50 86.36 288.58 96.15 0.2244E+01 0.2057E+02 -0.6452E+00 7 16.60 111.72 409.72 115.00 0.7333E+01 0.6611E+01 0.8197E+01 9 23.60 185.22 448.78 183.86 0.9625E+01 0.4766E+01 0.1042E+02 11 32.00 257.26 483.53 258.35 0.7328E+01 0.3623E+01 0.6722E+01 13 45.50 314.21 525.21 317.50 0.3110E+01 0.2660E+01 0.2924E+01 15 61.50 354.09 562.44 350.01 0.2070E+01 0.2052E+01 0.2023E+01 17 73.00 426.85 584.39 433.46 0.2655E+02 0.1773E+01 0.3012E+02 19 76.70 528.71 590.88 532.02 0.2868E+02 0.1700E+01 0.2250E+02 21 80.10 626.22 596.47 609.05 0.2517E+02 0.1639E+01 0.2280E+02 23 84.90 723.24 604.25 719.33 0.2021E+02 0.1560E+01 0.2314E+02 25 92.00 809.98 614.84 812.45 0.8132E+01 0.1459E+01 0.8046E+01 27 104.25 901.85 631.79 911.98 0.7106E+01 0.1314E+01 0.8120E+01 29 114.90 990.04 645.27 997.33 0.1114E+02 0.1211E+01 0.7875E+01 31 123.30 1063.54 655.10 1062.30 0.7351E+01 0.1142E+01 0.7587E+01 33 132.95 1138.88 665.78 1133.79 0.8364E+01 0.1073E+01 0.7230E+01 35 142.50 1211.65 675.88 1201.22 0.6997E+01 0.1012E+01 0.6898E+01 37 155.15 1284.79 688.10 1286.05 0.4933E+01 0.9440E+00 0.6529E+01 39 172.70 1359.75 703.94 1377.68 0.3784E+01 0.8640E+00 0.2476E+00 41 192.50 1384.37 720.29 1379.95 -0.1402E+01 0.7901E+00 0.7025E-02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18600000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.84941189E+02 0.10680167E+05 -0.70559240E+05 0.16635651E+06 -0.16849309E+06 Rj0 = 16.6000 39.0000 71.0000 75.0000 87.3000 169.4000 RKj = -0.23230984E+00 0.23472608E+01 0.26956347E+02 -0.79854910E+01 -0.15400121E+02 -0.59177646E+01



A.2 – 98


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 50

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

33

ta

column

99

beam pc pc pc pc qc

gc

132 165 198 231 264 297 330




66

gb

A.2 – 99


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.5604E+02 0.9496E+02 0.5821E+02 3 1.40 77.92 125.24 73.79 0.4653E+02 0.7736E+02 0.4218E+02 5 13.30 148.48 385.56 151.24 0.2363E+01 0.8177E+01 -0.1454E+00 7 28.17 172.97 468.94 170.94 0.1648E+01 0.4058E+01 0.2323E+01 9 41.45 202.13 513.99 205.56 0.2890E+01 0.2885E+01 0.2682E+01 11 53.45 256.52 544.91 254.90 0.6095E+01 0.2314E+01 0.5325E+01 13 66.25 317.71 571.88 315.02 0.3565E+01 0.1926E+01 0.4018E+01 15 81.17 352.19 598.19 360.24 0.1304E+01 0.1621E+01 0.2183E+01 17 97.70 373.75 622.95 385.66 0.2446E+02 0.1387E+01 0.9957E+00 19 101.30 479.95 627.91 481.40 0.3114E+02 0.1346E+01 0.2651E+02 21 104.30 577.46 631.92 560.72 0.3250E+02 0.1313E+01 0.2638E+02 23 108.17 674.73 636.96 662.42 0.2050E+02 0.1273E+01 0.2623E+02 25 112.90 771.76 642.78 786.24 0.1636E+02 0.1229E+01 0.2609E+02 27 122.00 848.20 653.61 856.72 0.8421E+01 0.1152E+01 0.7657E+01 29 134.70 955.50 667.79 952.95 0.8095E+01 0.1060E+01 0.7518E+01 31 143.50 1024.58 676.80 1018.91 0.7218E+01 0.1007E+01 0.7477E+01 33 155.80 1102.50 688.81 1110.73 0.8427E+01 0.9402E+00 0.7460E+01 35 163.30 1175.27 695.63 1166.69 0.8268E+01 0.9049E+00 0.7462E+01 37 175.60 1248.04 706.43 1258.54 0.5542E+01 0.8522E+00 0.7475E+01 39 190.00 1321.54 718.31 1315.59 0.4309E+01 0.7986E+00 0.3005E+01 41 204.53 1372.49 729.57 1359.38 0.3506E+01 0.7516E+00 0.3021E+01 43 217.60 1370.77 739.26 1398.93 -0.4688E+01 0.7139E+00 0.3032E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20133333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.63811479E+03 -0.44082834E+04 0.20476447E+05 -0.43316123E+05 0.38606337E+05 Rj0 = 0.0000 2.5000 47.3000 71.5000 97.7000 112.9000 178.7000 RKj = 0.67704419E+01 -0.96818873E+01 0.33081717E+01 -0.30203987E+00 0.25689238E+02 -0.18241020E+02 -0.44880891E+01



A.2 – 100


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 51

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

29

ta

column

87

beam pc pc pc pc qc

gc

116 145 174 203 232 261 290




58

gb

A.2 – 101


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7288E+02 0.9496E+02 0.7749E+02 3 1.30 77.17 117.38 77.94 0.4293E+02 0.7989E+02 0.4389E+02 5 9.43 121.64 348.09 122.41 0.1187E+01 0.1154E+02 -0.1100E+01 7 23.68 138.55 449.13 140.01 0.1187E+01 0.4753E+01 0.1200E+01 9 38.15 183.75 504.14 182.47 0.5000E+01 0.3102E+01 0.5139E+01 11 52.95 266.07 543.75 264.80 0.6117E+01 0.2333E+01 0.5636E+01 13 69.00 325.61 577.08 339.98 0.1624E+01 0.1861E+01 0.3440E+01 15 79.40 392.50 595.33 408.88 0.2940E+02 0.1652E+01 0.2517E+02 17 82.30 482.53 600.08 481.16 0.3374E+02 0.1602E+01 0.2467E+02 19 84.60 556.40 603.75 537.46 0.3063E+02 0.1565E+01 0.2429E+02 21 87.25 629.16 607.87 601.25 0.2484E+02 0.1525E+01 0.2386E+02 23 93.60 729.12 617.16 749.64 0.1277E+02 0.1438E+01 0.2290E+02 25 100.20 812.17 626.51 820.03 0.1119E+02 0.1357E+01 0.1024E+02 27 107.80 884.94 636.47 894.54 0.9857E+01 0.1277E+01 0.9398E+01 29 115.20 959.92 645.65 961.55 0.9321E+01 0.1208E+01 0.8739E+01 31 123.50 1029.73 655.33 1031.58 0.7928E+01 0.1141E+01 0.8163E+01 33 133.40 1102.50 666.26 1109.77 0.7210E+01 0.1070E+01 0.7662E+01 35 143.70 1175.27 676.95 1168.68 0.6591E+01 0.1006E+01 0.5551E+01 37 156.70 1253.17 689.56 1238.81 0.5427E+01 0.9363E+00 0.5262E+01 39 171.80 1325.21 703.16 1316.67 0.4173E+01 0.8677E+00 0.5071E+01 41 189.20 1385.84 717.81 1403.82 0.3485E+01 0.8008E+00 0.4960E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.17266667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.10119327E+04 -0.61902968E+04 0.12792470E+05 0.50178128E+04 -0.37095509E+05 Rj0 = 0.0000 2.3000 30.8000 60.4000 77.6000 93.6000 133.4000 RKj = 0.18539770E+01 -0.10348395E+02 0.37167784E+01 -0.34001318E+00 0.23517063E+02 -0.11784420E+02 -0.17513957E+01



A.2 – 102


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 52

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

30

ta

column

90

beam pc pc pc pc qc

gc

120 150 180 210 240 270 300




60

gb

A.2 – 103


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20141667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.29428361E+03 -0.37982615E+04 0.13258174E+05 0.28086046E+04 -0.50295948E+05 Rj0 = 3.1000 23.6000 65.6000 84.9000 103.0000 141.8000 RKj = -0.21951160E+02 0.27729796E+00 0.82782066E+01 0.25390050E+02 -0.91080026E+01 0.88623991E+00



A.2 – 104


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 53

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

32

ta

column

96

beam pc pc pc pc qc

gc

128 160 192 224 256 288 320




64

gb

A.2 – 105


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1158E+03 0.9496E+02 0.1107E+03 3 1.00 78.28 92.35 72.96 0.4422E+02 0.8652E+02 0.4305E+02 5 4.60 114.94 268.13 125.55 0.2037E+01 0.2518E+02 0.1115E+00 7 13.70 133.68 388.83 128.14 0.2052E+01 0.7942E+01 0.3958E+01 9 27.20 184.85 464.92 197.00 0.5624E+01 0.4188E+01 0.4968E+01 11 39.80 240.71 509.15 238.34 0.3124E+01 0.2989E+01 0.3589E+01 13 53.60 309.43 545.26 305.20 0.6408E+01 0.2309E+01 0.6359E+01 15 70.20 371.91 579.30 371.77 0.1420E+01 0.1833E+01 0.1593E+01 17 87.80 396.90 608.59 401.59 0.2253E+02 0.1518E+01 0.1545E+01 19 92.30 522.59 615.35 525.91 0.2975E+02 0.1455E+01 0.2754E+02 21 95.37 617.64 619.78 610.16 0.3100E+02 0.1415E+01 0.2740E+02 23 98.93 714.42 624.79 707.62 0.2422E+02 0.1372E+01 0.2725E+02 25 103.00 812.92 630.16 818.07 0.1896E+02 0.1327E+01 0.2707E+02 27 110.80 882.00 640.18 875.58 0.7602E+01 0.1249E+01 0.7220E+01 29 125.07 957.70 657.11 975.22 0.5306E+01 0.1129E+01 0.6778E+01 31 137.65 1049.39 670.85 1058.81 0.9879E+01 0.1042E+01 0.6528E+01 33 148.15 1139.25 681.44 1126.62 0.7132E+01 0.9804E+00 0.6396E+01 35 162.25 1230.76 694.68 1216.00 0.6132E+01 0.9097E+00 0.6292E+01 37 179.60 1323.37 709.95 1324.56 0.4472E+01 0.8359E+00 0.6231E+01 39 196.13 1356.32 723.26 1365.35 -0.5062E+00 0.7775E+00 -0.1323E+01 41 212.60 1347.98 735.63 1343.46 -0.5062E+00 0.7277E+00 -0.1334E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18716667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 9 AI = 0.22386121E+04 -0.17004689E+05 0.48662690E+05 -0.58343260E+05 0.26987414E+05 Rj0 = 0.4000 2.3000 20.6000 33.8000 45.8000 61.4000 87.8000 103.0000 187.9000 RKj = -0.23107083E+02 0.15287431E+02 0.12466641E+02 0.20866644E+01 -0.15909861E+00 -0.70202723E+01 0.26169329E+02 -0.19535683E+02 -0.75284642E+01



A.2 – 106


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 54

0.3125" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

30

ta

column

90

beam pc pc pc pc qc

gc

120 150 180 210 240 270 300




60

gb

A.2 – 107


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.5788E+02 0.9496E+02 0.7519E+02 3 1.50 78.28 132.87 81.38 0.4568E+02 0.7471E+02 0.3969E+02 5 5.40 147.73 286.52 147.91 0.9159E+01 0.2099E+02 0.2037E+01 7 19.67 197.22 428.41 192.52 0.3469E+01 0.5638E+01 0.3708E+01 9 33.20 259.09 487.83 259.64 0.5800E+01 0.3506E+01 0.5511E+01 11 45.45 327.81 525.07 327.73 0.5402E+01 0.2662E+01 0.5617E+01 13 58.90 378.16 557.00 376.62 0.2466E+01 0.2129E+01 0.2198E+01 15 73.83 412.58 585.82 413.32 0.2138E+01 0.1757E+01 0.2675E+01 17 88.50 443.94 609.65 454.00 0.2542E+02 0.1508E+01 0.2816E+01 19 91.77 543.90 614.54 543.67 0.3060E+02 0.1462E+01 0.2744E+02 21 95.10 644.10 619.37 635.11 0.2954E+02 0.1418E+01 0.2742E+02 23 98.50 744.55 624.16 728.28 0.2461E+02 0.1377E+01 0.2739E+02 25 102.00 812.92 628.81 824.06 0.1621E+02 0.1338E+01 0.2734E+02 27 110.30 882.00 639.55 886.46 0.7822E+01 0.1253E+01 0.7453E+01 29 120.50 955.50 651.87 961.61 0.7369E+01 0.1164E+01 0.7284E+01 31 133.50 1053.99 666.37 1054.97 0.7576E+01 0.1069E+01 0.7084E+01 33 147.40 1157.99 680.63 1152.19 0.7400E+01 0.9849E+00 0.6914E+01 35 160.95 1249.51 693.59 1245.02 0.5976E+01 0.9153E+00 0.6795E+01 37 175.70 1323.37 706.52 1341.02 0.4316E+01 0.8518E+00 0.8124E+00 39 189.25 1354.24 717.71 1351.67 -0.1263E+01 0.8012E+00 0.7631E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18183333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.29076022E+03 0.27129795E+04 -0.18068812E+05 0.44431940E+05 -0.47982576E+05 Rj0 = 0.0000 5.4000 51.3000 88.5000 102.0000 175.1000 RKj = -0.40704215E+01 0.96206349E+01 -0.38372854E+01 0.24638463E+02 -0.19766024E+02 -0.58969789E+01



A.2 – 108


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 55

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A


L.E.Thompson et al. (1970) C2-1 ALT


Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

31

ta

column

93

beam pc pc pc pc qc

gc

124 155 186 217 248 279 310




62

gb

A.2 – 109


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1298E+03 0.2120E+03 0.7425E+02 3 0.90 77.17 186.61 52.69 0.5350E+02 0.1971E+03 0.4478E+02 5 6.40 110.26 682.16 113.29 0.5254E+01 0.3882E+02 -0.1003E+01 7 16.60 147.00 914.53 144.45 0.3716E+01 0.1476E+02 0.5814E+01 9 35.50 221.23 1106.55 227.68 0.5064E+01 0.7371E+01 0.3534E+01 11 50.50 294.00 1200.69 285.61 0.3772E+01 0.5424E+01 0.4140E+01 13 60.90 330.76 1252.64 328.17 0.3350E+01 0.4619E+01 0.3941E+01 15 74.57 362.23 1310.46 376.42 0.1543E+01 0.3888E+01 0.3065E+01 17 88.70 384.04 1361.47 412.93 0.2716E+02 0.3358E+01 0.2140E+01 19 91.70 487.67 1371.47 488.75 0.3583E+02 0.3265E+01 0.2519E+02 21 94.50 579.17 1380.56 559.10 0.3032E+02 0.3183E+01 0.2506E+02 23 98.20 682.45 1392.24 651.51 0.2608E+02 0.3082E+01 0.2490E+02 25 103.80 790.86 1408.89 790.36 0.1533E+02 0.2944E+01 0.2470E+02 27 114.35 900.01 1438.70 921.09 0.7871E+01 0.2715E+01 0.6233E+01 29 126.35 992.25 1470.15 994.80 0.7424E+01 0.2497E+01 0.6071E+01 31 140.75 1084.13 1504.33 1081.50 0.5834E+01 0.2284E+01 0.5986E+01 33 157.50 1177.10 1541.13 1181.47 0.5185E+01 0.2079E+01 0.5958E+01 35 171.40 1250.60 1568.96 1247.77 0.5402E+01 0.1940E+01 0.3457E+01 37 185.80 1304.87 1596.03 1297.57 0.2387E+01 0.1815E+01 0.3461E+01 39 201.40 1342.10 1623.39 1351.60 0.2387E+01 0.1698E+01 0.3465E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.17533333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.12616871E+04 -0.92539293E+04 0.31198702E+05 -0.49539553E+05 0.34932742E+05 Rj0 = 0.9000 88.7000 107.3000 164.8000 RKj = 0.96593450E+00 0.23213840E+02 -0.18205631E+02 -0.24998156E+01



A.2 – 110


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 56

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

25

ta

column

75

beam pc pc pc pc qc

gc

100 125 150 175 200 225 250




50

gb

A.2 – 111


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.14958333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.32445663E+03 0.50684855E+04 -0.50920715E+05 0.15246565E+06 -0.18494286E+06 Rj0 = 0.0000 2.0000 26.2000 67.0000 81.6000 104.6000 RKj = 0.97980893E+01 -0.17088897E+02 0.28391690E+01 0.23420307E+02 -0.17611771E+02 0.26799252E+01



A.2 – 112


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 57

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

27

ta

column

81

beam pc pc pc pc qc

gc

108 135 162 189 216 243 270




54

gb

A.2 – 113


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4043E+03 0.2120E+03 0.1160E+03 3 0.60 76.63 126.03 57.75 0.7240E+02 0.2060E+03 0.7842E+02 5 3.00 122.09 484.51 142.60 0.4879E+01 0.9147E+02 0.8418E+01 7 6.80 140.65 697.11 138.60 0.4888E+01 0.3635E+02 -0.2193E+01 9 13.60 166.85 865.92 160.07 0.3487E+01 0.1787E+02 0.6125E+01 11 24.90 220.50 1015.43 232.41 0.6283E+01 0.1012E+02 0.5533E+01 13 37.95 294.37 1123.91 289.74 0.4819E+01 0.6955E+01 0.4021E+01 15 52.45 349.13 1211.08 346.80 0.2643E+01 0.5251E+01 0.3726E+01 17 65.80 390.29 1274.54 392.52 0.3083E+01 0.4324E+01 0.3154E+01 19 80.00 426.54 1330.96 435.50 0.2553E+01 0.3664E+01 0.2994E+01 21 88.25 483.26 1359.97 489.34 0.3355E+02 0.3373E+01 0.2808E+02 23 91.10 578.44 1369.52 569.45 0.3329E+02 0.3283E+01 0.2814E+02 25 94.75 688.69 1381.41 672.33 0.2751E+02 0.3176E+01 0.2824E+02 27 99.30 792.32 1395.40 801.09 0.1922E+02 0.3055E+01 0.2836E+02 29 107.20 898.90 1418.77 909.65 0.1068E+02 0.2865E+01 0.6624E+01 31 117.40 992.25 1446.89 978.57 0.7500E+01 0.2656E+01 0.6883E+01 33 129.65 1065.75 1478.10 1064.44 0.5000E+01 0.2445E+01 0.7123E+01 35 142.90 1138.15 1509.45 1145.32 0.6042E+01 0.2254E+01 0.4798E+01 37 156.85 1215.69 1539.47 1213.11 0.5205E+01 0.2088E+01 0.4909E+01 39 170.30 1280.00 1566.75 1279.58 0.4151E+01 0.1950E+01 0.4970E+01 --------------------------------------------------------------------------------------------------




A.2 – 114


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 58

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

28

ta

column

84

beam pc pc pc pc qc

gc

112 140 168 196 224 252 280




56

gb

A.2 – 115


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.16783333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.13379513E+04 -0.11229766E+05 0.44252744E+05 -0.79501320E+05 0.63086998E+05 Rj0 = 26.2500 74.0000 80.8000 100.6000 161.4000 RKj = -0.24466896E+01 0.34559634E+02 -0.17296991E+02 -0.10087633E+02 -0.28682584E+01



A.2 – 116


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 59

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

29

ta

column

87

beam pc pc pc pc qc

gc

116 145 174 203 232 261 290




58

gb

A.2 – 117


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1084E+03 0.2120E+03 0.7660E+02 3 1.25 78.46 253.02 73.07 0.4129E+02 0.1810E+03 0.4292E+02 5 4.50 121.92 592.80 137.22 0.3417E+01 0.5762E+02 0.5037E+01 7 11.80 147.00 831.49 132.28 0.2983E+01 0.2054E+02 0.3346E-01 9 29.10 183.01 1054.82 203.11 0.6192E+01 0.8804E+01 0.4983E+01 11 38.65 257.25 1128.69 254.86 0.7277E+01 0.6846E+01 0.5785E+01 13 51.40 330.75 1205.52 323.56 0.4773E+01 0.5343E+01 0.5118E+01 15 65.55 394.33 1273.45 393.53 0.4159E+01 0.4338E+01 0.4768E+01 17 79.77 446.39 1330.11 457.92 0.3249E+01 0.3673E+01 0.4256E+01 19 95.30 496.86 1382.97 518.68 0.2723E+02 0.3162E+01 0.3562E+01 21 97.70 571.09 1390.52 579.25 0.3113E+02 0.3096E+01 0.2519E+02 23 100.65 668.48 1399.60 653.38 0.3547E+02 0.3020E+01 0.2506E+02 25 103.65 760.36 1408.60 728.38 0.2761E+02 0.2946E+01 0.2494E+02 27 109.25 865.10 1424.59 867.44 0.1431E+02 0.2820E+01 0.2473E+02 29 116.40 957.34 1444.49 979.43 0.1135E+02 0.2673E+01 0.5685E+01 31 125.30 1031.57 1467.58 1028.89 0.6481E+01 0.2514E+01 0.5439E+01 33 137.85 1103.24 1497.64 1095.44 0.5109E+01 0.2324E+01 0.5183E+01 35 153.50 1176.01 1532.41 1174.84 0.4273E+01 0.2126E+01 0.4982E+01 37 169.25 1250.24 1564.81 1252.32 0.5242E+01 0.1960E+01 0.4868E+01 39 181.95 1312.71 1588.86 1313.80 0.4503E+01 0.1847E+01 0.4817E+01 --------------------------------------------------------------------------------------------------




A.2 – 118


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 2.5500" = -" = - X -

----

" " "

ta = cl = qc =

II - 60

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

25

ta

column

75

beam pc pc pc pc qc

gc

100 125 150 175 200 225 250




50

gb

A.2 – 119


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5





A.2 – 120


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 61

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

18

ta

column

54

beam pc pc pc pc qc

gc

72

90

108 126 144 162 180




36

gb

A.2 – 121


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10683333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.71631411E+03 -0.16926351E+03 -0.89711221E+04 0.23544237E+05 -0.20435029E+05 Rj0 = 3.0000 40.6000 74.0000 86.5000 RKj = 0.13091245E+02 -0.64977392E+01 0.35607281E+02 -0.32301638E+02



A.2 – 122


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 62

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

18

ta

column

54

beam pc pc pc pc qc

gc

72

90

108 126 144 162 180




36

gb

A.2 – 123


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10908333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.80183409E+03 -0.48353336E+04 0.16714098E+05 -0.27293535E+05 0.18079608E+05 Rj0 = 66.4000 75.3000 84.6000 RKj = 0.53285117E+02 -0.30437815E+02 -0.15235249E+02



A.2 – 124


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 63

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

20

ta

column

60

beam pc pc pc pc qc

gc

80

100 120 140 160 180 200




40

gb

A.2 – 125


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1223E+03 0.2223E+03 0.1172E+03 3 0.90 74.20 195.74 78.79 0.6253E+02 0.2067E+03 0.6238E+02 5 7.87 118.58 768.82 121.71 0.1077E+01 0.3262E+02 -0.4238E+01 7 20.60 132.30 1015.10 136.99 0.2706E+01 0.1265E+02 0.3417E+01 9 32.70 183.76 1138.01 188.66 0.8498E+01 0.8321E+01 0.5149E+01 11 39.60 259.09 1190.65 252.17 0.1028E+02 0.7030E+01 0.9434E+01 13 51.40 367.50 1264.49 362.19 0.6120E+01 0.5604E+01 0.8956E+01 15 63.30 403.51 1325.37 414.05 0.3026E+01 0.4688E+01 0.3633E+01 17 75.20 439.52 1377.15 449.05 0.4562E+02 0.4050E+01 0.2306E+01 19 77.53 565.46 1386.54 562.90 0.5397E+02 0.3945E+01 0.4869E+02 21 79.75 683.18 1395.23 670.62 0.5215E+02 0.3852E+01 0.4850E+02 23 82.10 795.64 1404.23 784.38 0.4438E+02 0.3758E+01 0.4832E+02 25 84.85 906.99 1414.49 916.99 0.3701E+02 0.3655E+01 0.4812E+02 27 88.20 1013.93 1426.31 1018.58 0.2805E+02 0.3540E+01 0.1672E+02 29 93.40 1104.34 1444.51 1104.84 0.1125E+02 0.3371E+01 0.1646E+02 31 100.15 1177.10 1466.55 1190.29 0.1033E+02 0.3180E+01 0.9032E+01 33 106.30 1249.87 1485.47 1245.30 0.1375E+02 0.3027E+01 0.8866E+01 35 113.00 1323.37 1505.49 1304.24 0.9096E+01 0.2874E+01 0.8738E+01 37 123.00 1388.42 1532.99 1390.98 0.4777E+01 0.2680E+01 0.8621E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.11500000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.62726472E+03 -0.49584357E+03 -0.87900708E+04 0.35812717E+05 -0.50159941E+05 Rj0 = 1.5000 32.7000 51.4000 75.2000 86.3000 96.7000 RKj = 0.45692665E+00 0.37170790E+01 -0.39250297E+01 0.46599788E+02 -0.31192543E+02 -0.71711048E+01



A.2 – 126


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 64

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

17

ta

column

51

beam pc pc pc pc qc

gc

68

85

102 119 136 153 170




34

gb

A.2 – 127


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.98500000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.11869952E+04 -0.73799885E+04 0.26073634E+05 -0.48377295E+05 0.44151185E+05 Rj0 = 1.6000 68.1000 85.1000 RKj = 0.73844694E+01 0.30186225E+02 -0.28783358E+02



A.2 – 128


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 65

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

17

ta

column

51

beam pc pc pc pc qc

gc

68

85

102 119 136 153 170




34

gb

A.2 – 129


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5





A.2 – 130


: :


1) 2)

= 11.5000" = 2.2500" = -" = - X 2

lu gc pc nc

= -" = 1.8000" = -" = - X -

----

" " "

ta = cl = qc =

II - 66

0.5000" -" -"

------------------------------


ll = cu = qb =

Major parameters


Remark

lp gb pb nb

U.S.A




Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

18

ta

column

54

beam pc pc pc pc qc

gc

72

90

108 126 144 162 180




36

gb

A.2 – 131


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10250000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.77817580E+02 0.14367129E+05 -0.96767098E+05 0.25052957E+06 -0.28160990E+06 Rj0 = 8.4000 66.9000 74.8000 91.8000 RKj = -0.93194222E+01 0.49334993E+02 -0.25101334E+02 -0.10808145E+02



A.2 – 132


: :


1) 2)

1.5000" 1.5000"

ll = cl =

7.3750" 1.5000"

0.3750" 3.0000"

II - 67

------------------------------


for beam web.

ta = pc =

Actual strength Fy = 50.0 ksi, Fu = 76.1 ksi No washers were used.

lu = cu =


Remark

lp = 9.0000" gc = 1.8325" nc = 1 X 3

Canada Fasteners: A325-X-3/4"D 15/16" Oversize holes Material : G40.12 Fy = 50.00 ksi Fu = 76.10 ksi

Major parameters

W.H.Sommer (1969) TEST21

Column : -Beam : W18X45 Angle : 3.5 X 3 X 3/8

Tested by Test Id.

Connection type : Double web-angle connections Mode : Welded-to-beam and bolted-to-column

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0


12

36

48

60

72


24

qc

84

pc pc pc pc

Material : G40.12 Fy = 50.00 ksi : Experimental : Polynominal : M. Exponential : Power model, n = 0.50

ta

column

96

gc

108 120

A.2 – 133


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



-0.90571919E+03

-5






A.2 – 134


: :


1) 2)

1.5000" 1.5000"

ll = cl =

4.3750" 1.5000"

0.3750" 3.0000"

II - 68

------------------------------


for beam web.

ta = pc =


lu = cu =


Remark

lp = 12.0000" gc = 1.8325" nc = 1 X 4


Major parameters


Column : -Beam : W18X45 Angle : 3.5 X 3 X 3/8

Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0


15

45

60

75

90


30

qc

gc

105 120 135 150

pc pc pc pc


ta

column

A.2 – 135


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.38230398E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5893E+02 0.1463E+03 0.5311E+02 0.1801E+04 3 1.87 110.00 244.03 109.92 361.85 0.5893E+02 0.9986E+02 0.5899E+02 0.6232E+02 5 4.30 237.50 400.99 241.24 456.21 0.4833E+02 0.4189E+02 0.4811E+02 0.2510E+02 7 7.90 383.00 506.58 386.64 518.41 0.3476E+02 0.2137E+02 0.3363E+02 0.1216E+02 9 12.15 504.50 578.79 504.90 557.64 0.2256E+02 0.1377E+02 0.2304E+02 0.7087E+01 11 18.37 601.33 648.42 608.46 591.17 0.1189E+02 0.9255E+01 0.1222E+02 0.4149E+01 13 26.50 698.00 711.56 689.89 617.51 0.9224E+01 0.6609E+01 0.8692E+01 0.2548E+01 15 33.60 747.00 753.64 749.27 632.89 0.6255E+01 0.5346E+01 0.8177E+01 0.1848E+01 17 42.40 795.00 796.01 793.72 646.74 0.4442E+01 0.4357E+01 0.4700E+01 0.1344E+01 19 52.13 827.33 834.71 832.56 658.07 0.3322E+01 0.3643E+01 0.3151E+01 0.1010E+01 21 61.87 859.66 867.62 853.88 666.79 0.3322E+01 0.3146E+01 0.1235E+01 0.7959E+00 23 71.60 892.00 896.36 857.49 673.77 0.9191E+01 0.2778E+01 -0.4200E+00 0.6486E+00 25 75.60 989.00 907.35 1012.59 676.27 0.4226E+02 0.2651E+01 0.3851E+02 0.6008E+00 27 78.00 1090.00 913.67 1104.66 677.68 0.4503E+02 0.2582E+01 0.3822E+02 0.5750E+00 29 79.90 1180.00 918.55 1177.09 678.76 0.4554E+02 0.2529E+01 0.3802E+02 0.5558E+00 31 82.70 1300.00 925.37 1283.15 680.27 0.4077E+02 0.2459E+01 0.3775E+02 0.5294E+00 33 86.10 1430.00 933.66 1410.99 682.02 0.3207E+02 0.2376E+01 0.3746E+02 0.5001E+00 35 89.60 1520.00 941.90 1541.67 683.73 0.1809E+02 0.2297E+01 0.3722E+02 0.4727E+00 37 95.65 1520.00 955.33 1519.96 686.46 -0.3922E+01 0.2175E+01 -0.3742E+01 0.4309E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10516583E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.26461235E+03 0.38699400E+04 -0.25342389E+05 0.72286486E+05 -0.87772700E+05 Rj0 = 0.0000 5.8000 14.3000 33.6000 71.6000 89.6000 RKj = 0.18294939E+01 0.65414756E+00 -0.28790736E+01 -0.28960281E+01 0.39473061E+02 -0.40632824E+02



A.2 – 136


: :


1) 2)

1.5000" 1.5000"

ll = cl =

7.3750" 1.5000"

0.3750" 3.0000"

II - 69

------------------------------


for beam web.

ta = pc =


lu = cu =


Remark

lp = 15.0000" gc = 2.5300" nc = 1 X 5


Major parameters


Column : -Beam : W24X76 Angle : 4 X 3 X 3/8

Tested by Test Id.


0

300

600

900

1200

1500

1800

2100

2400

2700

3000

0


14

42

56

70

84

gc


28

qc

98

pc pc pc pc


ta

column

A.2 – 137


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.34419691E+05

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10325000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.12553982E+03 0.19219360E+04 -0.18196636E+05 0.60158318E+05 -0.77104029E+05 Rj0 = 0.0000 6.0000 14.9000 67.0000 76.0000 RKj = 0.11846132E+01 -0.48141453E+01 0.33930542E+01 0.11036930E+03 -0.88439560E+02



A.2 – 138


: :


1) 2)

1.5000" 1.5000"

ll = cl =

4.3750" 1.5000"

0.3750" 3.0000"

II - 70

------------------------------


for beam web.

ta = pc =

Actual strength fy = 51.5 ksi, fu = 77.9 ksi No washers were used.

lu = cu =


Remark

lp = 18.0000" gc = 2.5300" nc = 1 X 6


Major parameters


Column : -Beam : W24X76 Angle : 4 X 3 X 3/8

Tested by Test Id.


0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

13

ta

column

39

beam pc pc pc pc qc

gc

52

65

78

91

104 117 130




26

gb

A.2 – 139


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.23774134E+05

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.89750000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.10611872E+04 0.12142415E+05 -0.47536429E+05 0.84924804E+05 -0.71717757E+05 Rj0 = 0.0000 7.3000 11.5000 23.6000 69.7000 RKj = 0.58878830E+02 -0.36328754E+02 -0.16483134E+02 0.21707644E+01 0.32403594E+02



A.2 – 140


: :


lu gc pc nc

= 1.1811" = 1.3819" = 3.9370" = 2 X 2

ll = cu = qc =

1.1811" 1.1811" -"

ta = cl =

0.3150" 1.1811"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 86.04 60.00 27 86.04 62.31 28 86.04 64.00

1) Bolts were tightened to a torque of 160 Nm 2) Random bolt tightness & minor axis connection

= 6.2992" = 2.1650" = 3.9370" = 1 X 2


Remark

lp gb pb nb

Major parameters

II - 71

United Kingdom

Fasteners: 10.9- -M16 23/32" Oversize holes Material : -Fy = -ksi Fu = -ksi

J.B.Davison et al (1987) JT/01B

Column : UC 152x152x23 Beam : UB 254x102x22 Angle : RSA 80x60x8

Tested by Test Id.


0

15

30

45

60

75

90

105

120

135

150

0

gb

10

lu cu pb pb pb lp pb cl qb ll beam

40

50

60

qc

70

pc pc pc pc


30

: -Experimental Polynominal M. Exponential

20

Material : : :

ta

column

80

gc

90

100

A.2 – 141


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1907E+02 0.2376E+02 0.2843E+02 2 1.15 22.00 26.38 21.96 0.1353E+02 0.2085E+02 0.1184E+02 3 2.31 31.22 46.17 30.85 0.5789E+01 0.1349E+02 0.4599E+01 4 4.62 34.41 67.19 35.56 0.1527E+01 0.6275E+01 0.8054E+00 5 7.50 39.33 80.85 37.87 0.1113E+01 0.3668E+01 0.1046E+01 6 9.81 40.81 88.20 40.88 0.1065E+01 0.2771E+01 0.1526E+01 7 12.12 44.25 93.93 44.74 0.1586E+01 0.2243E+01 0.1785E+01 8 15.00 49.16 99.75 50.04 0.1941E+01 0.1822E+01 0.1853E+01 9 17.31 54.08 103.67 54.26 0.2130E+01 0.1590E+01 0.1789E+01 10 19.62 59.00 107.12 58.26 0.1941E+01 0.1414E+01 0.1672E+01 11 22.50 63.91 110.95 62.83 0.1349E+01 0.1246E+01 0.1493E+01 12 24.81 66.37 113.70 66.10 0.9587E+00 0.1140E+01 0.1342E+01 13 27.12 68.34 116.22 69.03 0.9280E+00 0.1052E+01 0.1194E+01 14 30.00 71.29 119.12 72.21 0.1046E+01 0.9603E+00 0.1019E+01 15 32.31 73.75 121.26 74.42 0.1332E+01 0.8990E+00 0.8904E+00 16 34.62 77.43 123.27 76.33 0.1077E+01 0.8456E+00 0.7727E+00 17 37.50 78.66 125.63 78.37 0.1894E+00 0.7880E+00 0.6417E+00 18 39.81 78.66 127.40 78.73 0.1544E-15 0.7478E+00 0.1110E+00 19 42.12 78.66 129.08 78.89 0.0000E+00 0.7119E+00 0.2968E-01 20 45.00 78.66 131.08 78.84 0.0000E+00 0.6720E+00 -0.5778E-01 21 47.31 78.66 132.59 78.64 0.1544E-15 0.6435E+00 -0.1174E+00 22 49.62 78.66 134.08 78.31 0.3787E+00 0.6170E+00 -0.1688E+00 23 52.50 81.12 135.79 81.34 0.9706E+00 0.5881E+00 0.1026E+01 24 54.81 83.58 137.14 83.66 0.1065E+01 0.5664E+00 0.9898E+00 25 57.12 86.04 138.40 85.91 0.5918E+00 0.5470E+00 0.5477E-01 26 60.00 86.04 139.95 86.02 0.0000E+00 0.5244E+00 0.2333E-01 27 62.31 86.04 141.16 86.05 -0.8674E-18 0.5075E+00 0.2705E-02 28 64.00 86.04 142.02 86.04 0.0000E+00 0.4959E+00 -0.1022E-01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.82180833E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.67676542E+02 -0.88134591E+01 -0.30327239E+03 0.10943033E+04 -0.18560520E+04 Rj0 = 37.5000 49.6200 57.1100 RKj = -0.43869604E+00 0.12486624E+01 -0.90457423E+00



A.2 – 142


: :


1) 2)

lu gc pc nc

= 1.1811" = 1.3819" = 3.9370" = 2 X 2

Minor axis connection

= 6.2992" = 2.1650" = 3.9370" = 1 X 2


Remark

lp gb pb nb

1.1811" 1.1811" -"

ta = cl =

0.3150" 1.1811"

------------------------------


ll = cu = qc =

Major parameters

II - 72

United Kingdom


J.B.Davison et al (1987) JT/06

Column : UC 152x152x23 Beam : UB 254x102x22 Angle : RSA 80x60x8

Tested by Test Id.


0

15

30

45

60

75

90

105

120

135

150

0

gb

10

lu cu pb pb pb lp pb cl qb ll beam

40

50

60

qc

70

pc pc pc pc


30


20

Material : : :

ta

column

80

gc

90

100

A.2 – 143


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.57811667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.36357639E+02 -0.25728135E+03 0.15758341E+04 -0.30939628E+04 0.22923441E+04 Rj0 = 5.7700 15.8700 31.7300 60.5700 62.3100 RKj = 0.14315325E+00 0.19786299E+00 0.99844468E-01 0.71093257E+00 0.31904206E+01



A.2 – 144


: :


1) 2)

3.7402" 1.3779"

ll = cl =

3.7402" 1.3779"

ta = pc =

0.2756" 2.7559"

II - 73

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 121.81 22.92 27 121.18 23.98 28 122.59 25.08 29 123.22 26.21 30 126.05 27.19

Actual strength Fy = 872.2 N/mm2, Fu = 925.1 N/mm2 for high strength bolt. All bolts were tightened with 539 N-m torque (axial bolt tensile load: 147kN)

lu = cu =

Major parameters


Remark

lp = 8.2677" gc = 2.5590" nc = 1 X 3

Korea

Fasteners: F10T- -M20 7/8" Oversize holes Material : -Fy = 46.20 ksi Fu = 68.08 ksi

J.G. Yang and G.Y. Lee (2007) 3B-L-7-65

Column : H350x350x12x19 Beam : H400x200x8x13 Angle : L125x75x7

Tested by Test Id.


0

20

40

60

80

100

120

140

160

180

200

0

5

ta

column

15

beam pc pc pc pc qc

gc

20

25

30

35

40

45




10

gb

50

A.2 – 145


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.57082826E+04

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2185E+02 0.3273E+02 0.1505E+02 0.8373E+01 2 0.61 13.39 19.86 13.04 5.13 0.2131E+02 0.3175E+02 0.2352E+02 0.8358E+01 3 1.20 25.67 37.75 25.99 10.06 0.1900E+02 0.2833E+02 0.1961E+02 0.8320E+01 4 2.04 39.47 58.34 39.50 16.99 0.1370E+02 0.2078E+02 0.1315E+02 0.8233E+01 5 2.75 47.48 71.05 47.66 22.77 0.1059E+02 0.1555E+02 0.1034E+02 0.8131E+01 6 3.49 54.71 81.13 54.82 28.73 0.9784E+01 0.1191E+02 0.9258E+01 0.7999E+01 7 4.22 61.94 89.00 61.52 34.58 0.1050E+02 0.9560E+01 0.8922E+01 0.7845E+01 8 4.77 67.91 93.82 66.30 38.80 0.8265E+01 0.8331E+01 0.8722E+01 0.7719E+01 9 5.47 71.21 99.25 72.32 44.18 0.6233E+01 0.7129E+01 0.8296E+01 0.7541E+01 10 6.28 77.65 104.56 78.71 50.16 0.7895E+01 0.6124E+01 0.7535E+01 0.7322E+01 11 6.90 82.52 108.19 83.18 54.68 0.7696E+01 0.5524E+01 0.6801E+01 0.7142E+01 12 7.61 87.87 111.89 87.67 59.64 0.6727E+01 0.4976E+01 0.5908E+01 0.6931E+01 13 8.36 92.27 115.46 91.78 64.79 0.5246E+01 0.4504E+01 0.4975E+01 0.6697E+01 14 9.10 95.72 118.64 95.14 69.65 0.4385E+01 0.4124E+01 0.4153E+01 0.6464E+01 15 10.22 100.12 122.98 99.19 76.67 0.2939E+01 0.3664E+01 0.3157E+01 0.6107E+01 16 11.22 102.17 126.48 102.02 82.62 0.1333E+01 0.3335E+01 0.2528E+01 0.5786E+01 17 12.14 102.80 129.43 104.15 87.81 0.1678E+01 0.3084E+01 0.2142E+01 0.5495E+01 18 13.16 105.62 132.44 106.19 93.24 0.2786E+01 0.2849E+01 0.1878E+01 0.5180E+01 19 14.62 109.71 136.40 108.77 100.49 0.1766E+01 0.2573E+01 0.1689E+01 0.4745E+01 20 15.78 110.81 139.29 110.70 105.83 0.1088E+01 0.2390E+01 0.1621E+01 0.4415E+01 21 16.93 112.22 141.94 112.53 110.72 0.1572E+01 0.2236E+01 0.1575E+01 0.4108E+01 22 18.08 114.42 144.43 114.32 115.28 0.1487E+01 0.2102E+01 0.1526E+01 0.3818E+01 23 19.30 115.68 146.91 116.13 119.74 0.1276E+01 0.1978E+01 0.1458E+01 0.3532E+01 24 20.45 117.41 149.12 117.76 123.65 0.1930E+01 0.1874E+01 0.1375E+01 0.3280E+01 25 21.69 120.39 151.40 119.41 127.58 0.1767E+01 0.1775E+01 0.1268E+01 0.3026E+01 26 22.92 121.81 153.53 120.90 131.17 0.2061E+00 0.1687E+01 0.1149E+01 0.2795E+01 27 23.98 121.18 155.30 122.05 134.01 0.3221E+00 0.1618E+01 0.1042E+01 0.2613E+01 28 25.08 122.59 157.01 123.14 136.78 0.9256E+00 0.1554E+01 0.9308E+00 0.2436E+01 29 26.21 123.22 158.77 124.13 139.45 0.1794E+01 0.1492E+01 0.8189E+00 0.2267E+01 30 27.19 126.05 160.18 124.89 141.61 0.2871E+01 0.1445E+01 0.7263E+00 0.2131E+01 ----------------------------------------------------------------------------------------------------------------------------





A.2 – 146


: :


1) 2)

2.3623" 1.3779"

ll = cl =

2.3623" 1.3779"

ta = pc =

0.2756" 2.7559"

II - 74

------------------------------



lu = cu =

Major parameters


Remark

lp = 11.0236" gc = 2.5590" nc = 1 X 4

Korea




Tested by Test Id.


0

30

60

90

120

150

180

210

240

270

300

0

3

ta

column

9

beam pc pc pc pc qc

gc

12

15

18

21

24

27




6

gb

30

A.2 – 147


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.87577342E+04

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4284E+02 0.6528E+02 0.3949E+02 0.1858E+02 2 0.60 25.65 38.72 25.29 11.12 0.3768E+02 0.6343E+02 0.3934E+02 0.1857E+02 3 1.27 47.08 79.08 47.41 23.59 0.2769E+02 0.5540E+02 0.2733E+02 0.1851E+02 4 1.93 62.57 111.61 63.45 35.70 0.2459E+02 0.4343E+02 0.2271E+02 0.1841E+02 5 2.52 77.61 134.32 76.71 46.53 0.2435E+02 0.3396E+02 0.2251E+02 0.1827E+02 6 3.11 91.32 152.21 90.17 57.26 0.2170E+02 0.2707E+02 0.2307E+02 0.1808E+02 7 3.75 104.15 167.76 104.92 68.75 0.2096E+02 0.2188E+02 0.2287E+02 0.1783E+02 8 4.45 119.63 181.72 120.57 81.20 0.2259E+02 0.1796E+02 0.2127E+02 0.1749E+02 9 5.03 132.90 191.32 132.20 91.15 0.2003E+02 0.1564E+02 0.1919E+02 0.1716E+02 10 5.67 143.51 200.67 143.63 102.00 0.1601E+02 0.1368E+02 0.1650E+02 0.1676E+02 11 6.21 151.91 207.70 151.94 110.97 0.1422E+02 0.1236E+02 0.1422E+02 0.1639E+02 12 6.91 160.74 215.92 160.99 122.35 0.9942E+01 0.1100E+02 0.1153E+02 0.1586E+02 13 7.47 165.14 221.80 166.90 131.07 0.1083E+02 0.1012E+02 0.9729E+01 0.1541E+02 14 8.04 173.10 227.39 172.04 139.78 0.1088E+02 0.9356E+01 0.8215E+01 0.1494E+02 15 8.68 177.94 233.13 176.85 149.15 0.7147E+01 0.8636E+01 0.6908E+01 0.1438E+02 16 9.34 182.34 238.59 181.04 158.40 0.5634E+01 0.8009E+01 0.5925E+01 0.1380E+02 17 9.90 184.97 242.92 184.17 165.95 0.3460E+01 0.7548E+01 0.5316E+01 0.1330E+02 18 10.55 186.27 247.71 187.48 174.48 0.4604E+01 0.7073E+01 0.4798E+01 0.1270E+02 19 11.13 190.23 251.67 190.13 181.62 0.4925E+01 0.6706E+01 0.4471E+01 0.1218E+02 20 11.77 191.97 255.84 192.90 189.22 0.3175E+01 0.6343E+01 0.4196E+01 0.1160E+02 21 12.37 194.16 259.59 195.38 196.10 0.4796E+01 0.6035E+01 0.3989E+01 0.1106E+02 22 12.96 197.68 263.07 197.69 202.48 0.5403E+01 0.5765E+01 0.3813E+01 0.1055E+02 23 13.60 200.75 266.67 200.07 209.05 0.3401E+01 0.5501E+01 0.3634E+01 0.1000E+02 24 14.28 202.04 270.29 202.45 215.59 0.3361E+01 0.5250E+01 0.3447E+01 0.9452E+01 25 14.85 204.68 273.30 204.38 220.88 0.4068E+01 0.5050E+01 0.3282E+01 0.8996E+01 26 15.47 206.86 276.33 206.37 226.34 0.2451E+01 0.4859E+01 0.3095E+01 0.8519E+01 27 16.06 207.72 279.20 208.14 231.24 0.3202E+01 0.4685E+01 0.2913E+01 0.8085E+01 28 16.54 209.91 281.35 209.49 235.01 0.4611E+01 0.4560E+01 0.2763E+01 0.7749E+01 ----------------------------------------------------------------------------------------------------------------------------





A.2 – 148


: :


1) 2)

0.9843" 1.3779"

ll = cl =

0.9843" 1.3779"

ta = pc =

0.2756" 2.7559"

II - 75

------------------------------



lu = cu =

Major parameters


Remark

lp = 13.7795" gc = 2.5590" nc = 1 X 4

Korea




Tested by Test Id.


0

35

70

105

140

175

210

245

280

315

350

0

3

ta

column

9

beam pc pc pc pc qc

gc

12

15

18

21

24

27




6

gb

30

A.2 – 149


Moment ( kip-inch )

R t A3 P3


( R : X 1/1000 radians )

-3

Q3 =



0.11059846E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.8827E+02 0.1115E+03 0.9896E+02 0.3514E+02 2 0.35 30.97 39.01 31.39 12.28 0.8156E+02 0.1105E+03 0.7822E+02 0.3477E+02 3 0.63 52.36 69.72 50.83 21.98 0.6100E+02 0.1080E+03 0.6091E+02 0.3433E+02 4 0.93 65.63 100.89 66.74 32.01 0.4448E+02 0.1032E+03 0.4807E+02 0.3379E+02 5 1.42 87.02 148.63 87.40 48.37 0.4014E+02 0.9031E+02 0.3798E+02 0.3278E+02 6 2.11 111.36 203.30 112.26 70.39 0.3744E+02 0.6891E+02 0.3532E+02 0.3125E+02 7 2.65 132.74 237.08 131.42 87.15 0.3724E+02 0.5496E+02 0.3452E+02 0.2997E+02 8 3.17 151.18 262.94 148.88 102.40 0.3107E+02 0.4521E+02 0.3251E+02 0.2876E+02 9 3.80 167.40 288.67 168.22 120.09 0.2601E+02 0.3676E+02 0.2855E+02 0.2729E+02 10 4.34 181.42 306.82 182.43 134.32 0.2402E+02 0.3162E+02 0.2470E+02 0.2608E+02 11 5.00 195.43 326.05 197.20 151.05 0.1974E+02 0.2691E+02 0.2019E+02 0.2463E+02 12 5.64 207.23 342.26 209.02 166.50 0.1809E+02 0.2348E+02 0.1658E+02 0.2326E+02 13 6.26 218.29 355.93 218.42 180.48 0.1732E+02 0.2093E+02 0.1398E+02 0.2202E+02 14 6.88 228.61 368.21 226.44 193.71 0.1321E+02 0.1889E+02 0.1212E+02 0.2084E+02 15 7.48 234.51 379.10 233.35 205.95 0.1049E+02 0.1726E+02 0.1084E+02 0.1974E+02 16 8.20 242.63 390.87 240.70 219.65 0.9162E+01 0.1567E+02 0.9768E+01 0.1852E+02 17 8.80 247.05 399.98 246.38 230.53 0.8588E+01 0.1455E+02 0.9084E+01 0.1756E+02 18 9.26 251.47 406.54 250.48 238.50 0.8262E+01 0.1380E+02 0.8627E+01 0.1685E+02 19 9.81 255.16 413.87 255.06 247.50 0.6737E+01 0.1301E+02 0.8118E+01 0.1606E+02 20 10.36 258.85 420.80 259.37 256.09 0.5857E+01 0.1231E+02 0.7618E+01 0.1531E+02 21 10.96 261.80 428.02 263.80 265.09 0.7332E+01 0.1163E+02 0.7059E+01 0.1454E+02 22 11.56 267.70 434.86 267.89 273.64 0.6721E+01 0.1102E+02 0.6490E+01 0.1380E+02 23 12.17 269.91 441.34 271.63 281.76 0.5609E+01 0.1048E+02 0.5914E+01 0.1312E+02 24 12.76 274.34 447.38 274.95 289.31 0.3661E+01 0.1001E+02 0.5355E+01 0.1249E+02 25 13.32 274.34 453.00 277.81 296.16 0.3981E+01 0.9584E+01 0.4833E+01 0.1192E+02 26 13.94 279.50 458.67 280.63 303.33 0.6979E+01 0.9179E+01 0.4282E+01 0.1133E+02 27 14.61 283.19 464.72 283.32 310.76 0.7657E+01 0.8770E+01 0.3718E+01 0.1073E+02 28 15.16 288.35 469.52 285.24 316.51 0.6741E+01 0.8460E+01 0.3292E+01 0.1027E+02 29 15.99 290.56 476.27 287.72 324.75 0.2672E+01 0.8046E+01 0.2710E+01 0.9628E+01 ----------------------------------------------------------------------------------------------------------------------------





A.2 – 150



1) 2)

lu = 1.3750" gc = 2.6250" pc = 3.0000" tt = 0.3125" gt’= 2.0000" rt = 3.5000" ps = 2.5000" nt’= 2 X 1 ns’= 2 X

1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3125" gs’= 2.0000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs

Major parameters

Heavy hex high strength bolts used

= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

U.S.A.

Fasteners: A325- -3/4"D 13/16" Oversize holes Material : A36 Fy = 40.65 ksi Fu = 68.43 ksi

A.Azizinamini et al. (1985) 8S1

W12X58 W8X21 6 X 3.5 X 5/16 X 6.0 4 X 3.5 X 1/4 X 5.5

: :


Remark

lp gb pb lt gt qt pt nt

Column : Beam : F.Angle: W.Angle:

Tested by Test Id.

III Connection type : Top-and seat-angle connections with double web angle Mode : All bolted

1

0

50

100

150

200

250

300

350

400

450

500

0

7

gb

ta

column

pt

21

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

28

35

42

49

56

63

Material : A36 Fy = 40.65 ksi : Experimental : Polynominal : M. Exponential : Power model, n = 1.66

ll

lp

lu beam

gt'


14

gs

gt

70

ts

tt

A.3 – 1


Moment ( kip-inch )

R tc A3 P3

= Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.250000" w = 6.000000" g = 1.625000" = 3.188976 K = 0.242339 = 5 Q1 = -2 Q2 = -5

( R : X 1/1000 radians )

Q3 =



0.93013975E+04

-9




Frye and Morris polynominal model : t = 0.312500" d = 8.250000" A1 = 2.232429 A2 = 1.850728 P1 = 1 P2 = 3


A.3 – 2



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3750" gs’= 2.0000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

Major parameters

X 6.0 X 5.5

U.S.A.



W12X58 W8X21 6 X 3.5 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


2

0

50

100

150

200

250

300

350

400

450

500

0

5

gb

ta

column

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 3


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.34709931E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2407E+03 0.2271E+03 0.2791E+03 0.9802E+02 3 0.11 26.29 24.33 27.12 10.64 0.2405E+03 0.2147E+03 0.2207E+03 0.9675E+02 5 0.21 50.17 45.22 47.73 20.55 0.2208E+03 0.1888E+03 0.1804E+03 0.9504E+02 7 0.37 74.74 71.71 72.60 35.29 0.1271E+03 0.1487E+03 0.1387E+03 0.9202E+02 9 0.66 104.15 107.35 106.53 61.25 0.8517E+02 0.1005E+03 0.9978E+02 0.8586E+02 11 1.01 133.18 136.48 137.51 89.63 0.8266E+02 0.7143E+02 0.8232E+02 0.7839E+02 13 1.33 160.04 157.00 162.88 113.99 0.8573E+02 0.5615E+02 0.7429E+02 0.7162E+02 15 1.64 187.10 172.65 184.57 134.95 0.8858E+02 0.4685E+02 0.6761E+02 0.6566E+02 17 2.02 213.13 188.79 208.46 158.50 0.5535E+02 0.3898E+02 0.5846E+02 0.5891E+02 19 2.66 241.80 210.93 240.82 193.16 0.3220E+02 0.3048E+02 0.4217E+02 0.4904E+02 21 3.52 263.83 234.05 269.34 230.75 0.2571E+02 0.2377E+02 0.2540E+02 0.3868E+02 23 4.96 294.53 263.32 295.88 277.18 0.1680E+02 0.1758E+02 0.1434E+02 0.2680E+02 25 6.43 318.01 286.25 315.50 310.43 0.1528E+02 0.1402E+02 0.1303E+02 0.1916E+02 27 8.20 339.41 308.55 337.88 338.84 0.9786E+01 0.1134E+02 0.1188E+02 0.1337E+02 29 10.20 356.69 329.19 358.54 361.30 0.7368E+01 0.9383E+01 0.8499E+01 0.9354E+01 31 12.12 368.82 345.86 371.46 376.73 0.5264E+01 0.8091E+01 0.5094E+01 0.6926E+01 33 14.40 378.58 362.99 379.60 390.23 0.3583E+01 0.6978E+01 0.2299E+01 0.5046E+01 35 16.76 385.10 378.37 383.44 400.51 0.1697E+01 0.6131E+01 0.1210E+01 0.3778E+01 37 18.77 383.55 390.12 385.24 407.32 0.2715E+00 0.5566E+01 0.6570E+00 0.3024E+01 39 20.36 388.48 398.66 386.11 411.75 0.2107E+01 0.5194E+01 0.4628E+00 0.2570E+01 41 22.30 386.04 408.42 386.90 416.29 -0.1974E+01 0.4805E+01 0.3684E+00 0.2137E+01 43 24.09 385.38 416.75 387.53 419.83 0.2150E+00 0.4500E+01 0.3453E+00 0.1823E+01 45 26.91 388.59 428.80 388.51 424.42 0.1139E+01 0.4100E+01 0.3501E+00 0.1448E+01 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 4



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3125" gs’= 2.0000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 8.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs

Major parameters


= 5.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

U.S.A.



W12X58 W8X21 6 X 3.5 X 5/16 X 8.0 4 X 3.5 X 1/4 X 5.5

: :


Remark



Tested by Test Id.


3

0

60

120

180

240

300

360

420

480

540

600

0

6

gb

ta

column

pt

18

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

24

30

36

42

48

54


ll

lp

lu beam

gt'


12

gs

gt

60

ts

tt

A.3 – 5


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.72495441E+04

-9






A.3 – 6



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3750" gs’= 4.5000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

Major parameters

X 6.0 X 5.5

U.S.A.



W12X58 W8X21 6 X 6.0 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


4

0

25

50

75

100

125

150

175

200

225

250

0

7

gb

ta

column

pt

21

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

28

35

42

49

56

63


ll

lp

lu beam

gt'


14

gs

gt

70

ts

tt

A.3 – 7


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.11268508E+05

-9






A.3 – 8



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3750" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 8.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 5.5

U.S.A.



W12X58 W8X21 6 X 4.0 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


5

0

50

100

150

200

250

300

350

400

450

500

0

7

gb

ta

column

pt

21

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

28

35

42

49

56

63


ll

lp

lu beam

gt'


14

gs

gt

70

ts

tt

A.3 – 9


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.85258295E+03

-9






A.3 – 10



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3125" gs’= 2.5000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 2.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs

Major parameters


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 2.5000" = 2.7500" = 2.5000" = 2 X 2

U.S.A.



W12X58 W8X21 6 X 4.0 X 5/16 X 6.0 4 X 3.5 X 1/4 X 5.5

: :


Remark



Tested by Test Id.


6

0

35

70

105

140

175

210

245

280

315

350

0

7

gb

ta

column

pt

21

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

28

35

42

49

56

63


ll

lp

lu beam

gt'


14

gs

gt

70

ts

tt

A.3 – 11


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.10866420E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.6003E+02 0.1287E+03 0.6526E+02 0.2210E+02 3 0.38 22.97 41.69 21.70 8.46 0.5144E+02 0.8273E+02 0.4947E+02 0.2210E+02 5 0.79 40.34 67.86 39.78 17.56 0.3848E+02 0.4930E+02 0.3926E+02 0.2210E+02 7 1.56 64.48 95.71 65.73 34.44 0.3201E+02 0.2773E+02 0.3013E+02 0.2210E+02 9 2.09 81.56 108.54 80.82 46.13 0.2968E+02 0.2143E+02 0.2717E+02 0.2208E+02 11 3.12 107.07 127.01 106.97 69.00 0.2459E+02 0.1498E+02 0.2338E+02 0.2198E+02 13 4.23 131.02 141.45 130.65 93.16 0.1905E+02 0.1146E+02 0.1938E+02 0.2165E+02 15 5.41 150.30 153.50 150.77 118.17 0.1379E+02 0.9243E+01 0.1492E+02 0.2087E+02 17 7.25 170.46 168.48 172.67 154.62 0.9563E+01 0.7148E+01 0.9166E+01 0.1826E+02 19 9.98 191.35 185.39 191.16 196.14 0.6017E+01 0.5420E+01 0.5206E+01 0.1190E+02 21 13.36 208.11 201.46 207.02 223.87 0.4164E+01 0.4219E+01 0.4560E+01 0.5165E+01 23 17.23 223.70 216.07 224.63 236.19 0.3890E+01 0.3393E+01 0.4415E+01 0.1796E+01 25 20.92 238.10 227.59 239.52 240.48 0.3907E+01 0.2876E+01 0.3552E+01 0.7110E+00 27 24.41 250.45 236.98 250.08 242.20 0.3173E+01 0.2523E+01 0.2499E+01 0.3281E+00 29 28.10 260.88 245.73 260.34 243.05 0.2523E+01 0.2241E+01 0.3051E+01 0.1598E+00 31 31.66 269.69 253.32 269.99 243.47 0.2414E+01 0.2026E+01 0.2408E+01 0.8610E-01 33 34.90 276.89 259.68 277.14 243.69 0.2020E+01 0.1865E+01 0.2033E+01 0.5183E-01 35 38.48 283.93 266.02 283.93 243.84 0.1928E+01 0.1719E+01 0.1786E+01 0.3113E-01 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 12



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3750" gs’= 2.5000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

Major parameters

X 6.0 X 5.5

U.S.A.



W12X58 W8X21 6 X 4.0 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


7

0

50

100

150

200

250

300

350

400

450

500

0

7

gb

ta

column

pt

21

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

28

35

42

49

56

63


ll

lp

lu beam

gt'


14

gs

gt

70

ts

tt

A.3 – 13


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.60937604E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4381E+02 0.1581E+03 0.4937E+02 0.3766E+02 3 0.53 23.22 64.71 25.73 19.96 0.5346E+02 0.8245E+02 0.4753E+02 0.3766E+02 5 1.25 59.81 106.07 58.88 47.14 0.4347E+02 0.4127E+02 0.4434E+02 0.3766E+02 7 2.06 93.56 132.65 93.42 77.63 0.3937E+02 0.2661E+02 0.4100E+02 0.3764E+02 9 2.77 121.38 149.09 121.39 104.20 0.3786E+02 0.2049E+02 0.3818E+02 0.3755E+02 11 3.89 161.05 168.71 161.49 145.94 0.3304E+02 0.1517E+02 0.3344E+02 0.3697E+02 13 4.81 189.66 181.43 190.41 179.48 0.3103E+02 0.1258E+02 0.2928E+02 0.3559E+02 15 5.98 221.59 194.75 221.49 219.03 0.2498E+02 0.1040E+02 0.2405E+02 0.3174E+02 17 7.68 257.15 210.60 256.60 265.15 0.1681E+02 0.8355E+01 0.1738E+02 0.2172E+02 19 10.09 290.94 228.44 289.99 300.04 0.1056E+02 0.6596E+01 0.1089E+02 0.8454E+01 21 12.65 310.32 243.70 312.46 312.80 0.6741E+01 0.5430E+01 0.7099E+01 0.2641E+01 23 15.54 328.09 258.06 329.45 317.17 0.5672E+01 0.4551E+01 0.4872E+01 0.7839E+00 25 18.91 344.97 272.12 343.13 318.67 0.4403E+01 0.3851E+01 0.3374E+01 0.2342E+00 27 22.61 359.05 285.31 357.49 319.19 0.3280E+01 0.3308E+01 0.4313E+01 0.7642E-01 29 26.13 370.20 296.27 371.21 319.36 0.3015E+01 0.2926E+01 0.3513E+01 0.3069E-01 31 29.36 379.73 305.27 381.66 319.43 0.2891E+01 0.2652E+01 0.2993E+01 0.1471E-01 33 32.68 389.56 313.67 390.96 319.47 0.3032E+01 0.2423E+01 0.2633E+01 0.7482E-02 35 35.57 398.07 320.48 398.26 319.48 0.2819E+01 0.2255E+01 0.2428E+01 0.4379E-02 37 38.53 406.57 326.95 405.21 319.49 0.2927E+01 0.2108E+01 0.2293E+01 0.2646E-02 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 14



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3125" gs’= 2.0000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs

Major parameters


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

U.S.A.



W12X58 W8X21 6 X 3.5 X 5/16 X 6.0 4 X 3.5 X 1/4 X 5.5

: :


Remark



Tested by Test Id.


8

0

55

110

165

220

275

330

385

440

495

550

0

6

gb

ta

column

pt

18

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

24

30

36

42

48

54


ll

lp

lu beam

gt'


12

gs

gt

60

ts

tt

A.3 – 15


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.39619303E+04

-9



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.38780667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.32502421E+02 -0.11554950E+03 0.33926834E+03 0.23135986E+04 -0.60854799E+04 Rj0 = 21.1800 RKj = 0.29969626E+01



A.3 – 16



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3750" gs’= 2.0000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

Major parameters

X 6.0 X 5.5

U.S.A.



W12X58 W8X21 6 X 3.5 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


9

0

60

120

180

240

300

360

420

480

540

600

0

6

gb

ta

column

pt

18

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

24

30

36

42

48

54


ll

lp

lu beam

gt'


12

gs

gt

60

ts

tt

A.3 – 17


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.12685490E+05

-9






A.3 – 18



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.5000" gs’= 2.0000" rs = 3.5000"

------------------------------


2

= 1.3750" = 1.2500" = 1 X 2 = 6.0000" = 3.5000" = 2.7500"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

Major parameters

X 6.0 X 5.5

U.S.A.



W12X58 W8X21 6 X 3.5 X 1/2 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.

III - 10 Connection type : Top-and seat-angle connections with double web angle Mode : All bolted

0

80

160

240

320

400

480

560

640

720

800

0

5

gb

ta

column

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 19


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.35098248E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5440E+03 0.3312E+03 0.5825E+03 0.3249E+03 3 0.10 55.05 32.97 52.81 30.83 0.5440E+03 0.3155E+03 0.4664E+03 0.2871E+03 5 0.24 113.47 74.48 110.43 68.96 0.3347E+03 0.2629E+03 0.3475E+03 0.2484E+03 7 0.48 171.78 125.95 175.99 120.97 0.1962E+03 0.1858E+03 0.2295E+03 0.2025E+03 9 0.75 222.11 168.92 227.98 170.98 0.1700E+03 0.1328E+03 0.1579E+03 0.1642E+03 11 1.02 267.92 200.39 265.26 211.39 0.1505E+03 0.1031E+03 0.1222E+03 0.1369E+03 13 1.58 329.71 247.96 322.50 276.69 0.9034E+02 0.7044E+02 0.8591E+02 0.9883E+02 15 2.46 382.05 298.41 381.77 347.20 0.4784E+02 0.4767E+02 0.5101E+02 0.6550E+02 17 3.65 419.90 345.81 422.74 409.79 0.2805E+02 0.3359E+02 0.2143E+02 0.4213E+02 19 5.06 453.34 386.71 442.92 458.16 0.6040E-01 0.2518E+02 0.1016E+02 0.2785E+02 21 6.75 455.91 423.96 458.36 496.57 0.1500E+02 0.1960E+02 0.8827E+01 0.1874E+02 23 8.74 485.59 458.78 483.28 527.44 0.1474E+02 0.1565E+02 0.1630E+02 0.1279E+02 25 10.80 511.80 488.11 513.99 549.79 0.1105E+02 0.1303E+02 0.1349E+02 0.9227E+01 27 12.82 535.91 512.49 538.67 566.01 0.1309E+02 0.1125E+02 0.1115E+02 0.7023E+01 29 14.62 559.49 531.63 557.51 577.38 0.1130E+02 0.1005E+02 0.9877E+01 0.5667E+01 31 16.75 579.09 551.87 575.19 588.19 0.7278E+01 0.8943E+01 0.7956E+01 0.4518E+01 33 19.05 591.13 571.29 593.05 597.49 0.5245E+01 0.8016E+01 0.7674E+01 0.3639E+01 35 21.34 603.16 588.81 610.57 605.07 0.1208E+02 0.7277E+01 0.7613E+01 0.2996E+01 37 23.44 630.95 603.56 626.52 610.86 0.6110E+01 0.6718E+01 0.7619E+01 0.2549E+01 39 25.30 642.35 615.68 640.74 615.30 0.5128E+01 0.6297E+01 0.7636E+01 0.2231E+01 41 26.94 649.32 625.68 653.24 618.76 0.4268E+01 0.5973E+01 0.7649E+01 0.2000E+01 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 20



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 3 ts = 0.3750" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

90

180

270

360

450

540

630

720

810

900

0

5

gb

ta

column

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 21


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.10042707E+05

-9






A.3 – 22



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 3 ts = 0.5000" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 1/2 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 23


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.20560226E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4676E+03 0.5334E+03 0.4356E+03 0.3527E+03 3 0.21 98.56 105.51 79.24 62.11 0.3869E+03 0.4447E+03 0.3253E+03 0.2608E+03 5 0.72 196.43 264.42 207.48 171.95 0.2009E+03 0.2223E+03 0.2057E+03 0.1853E+03 7 1.19 295.04 349.26 294.42 250.45 0.1831E+03 0.1454E+03 0.1658E+03 0.1482E+03 9 1.62 364.71 404.07 361.61 309.47 0.1608E+03 0.1109E+03 0.1454E+03 0.1255E+03 11 2.28 449.62 466.72 449.08 383.88 0.1130E+03 0.8200E+02 0.1203E+03 0.1017E+03 13 3.01 527.30 519.45 527.62 451.16 0.9626E+02 0.6413E+02 0.9560E+02 0.8373E+02 15 3.82 595.44 565.87 595.44 512.66 0.6887E+02 0.5201E+02 0.7383E+02 0.6972E+02 17 4.69 648.51 607.04 651.76 568.18 0.5716E+02 0.4342E+02 0.5692E+02 0.5875E+02 19 5.76 704.56 649.53 704.57 625.62 0.4787E+02 0.3624E+02 0.4239E+02 0.4886E+02 21 7.96 776.22 718.46 774.04 717.35 0.2577E+02 0.2733E+02 0.2206E+02 0.3572E+02 23 9.92 816.96 767.01 816.29 779.66 0.1691E+02 0.2259E+02 0.2049E+02 0.2840E+02 25 11.85 847.41 807.36 847.31 829.38 0.1426E+02 0.1938E+02 0.1239E+02 0.2338E+02 27 13.04 849.79 829.54 860.18 855.71 -0.1805E+02 0.1785E+02 0.9504E+01 0.2098E+02 29 15.38 875.15 868.40 879.00 900.35 0.1068E+02 0.1550E+02 0.7157E+01 0.1732E+02 31 18.08 903.51 907.34 898.21 942.69 0.1180E+02 0.1350E+02 0.7400E+01 0.1427E+02 33 19.75 920.68 929.09 911.13 965.25 -0.4906E+01 0.1252E+02 0.8096E+01 0.1280E+02 35 21.46 921.43 949.75 925.65 986.06 0.1029E+02 0.1167E+02 0.8855E+01 0.1154E+02 37 23.59 943.32 973.83 945.40 1009.18 0.1043E+02 0.1076E+02 0.9663E+01 0.1023E+02 39 25.66 965.21 995.29 966.04 1029.25 0.1057E+02 0.1002E+02 0.1024E+02 0.9184E+01 41 27.83 989.07 1016.39 988.82 1048.21 0.1131E+02 0.9355E+01 0.1066E+02 0.8260E+01 43 30.12 1014.91 1037.04 1013.51 1066.12 0.1131E+02 0.8754E+01 0.1093E+02 0.7445E+01 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 24



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 2 ts = 0.3750" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 4.3125" = 1.2500" = 1 X 2 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 5.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 5.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

85

170

255

340

425

510

595

680

765

850

0

5

gb

ta

column

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 25


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.70574845E+04

-9






A.3 – 26



1) 2)


1

ta = 0.3750" cl = 1.2500" nc = 1 X 3 ts = 0.3750" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 3/8 4 X 3.5 X 3/8

: :


Remark



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 27


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.33376875E+03

-9






A.3 – 28



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 3 ts = 0.3750" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 3/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 29


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.23930773E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5465E+03 0.4015E+03 0.4877E+03 0.1709E+03 3 0.18 97.71 68.48 74.92 30.57 0.4240E+03 0.3498E+03 0.3589E+03 0.1709E+03 5 0.52 163.13 162.03 171.05 88.62 0.1961E+03 0.2125E+03 0.2253E+03 0.1709E+03 7 0.95 249.83 234.03 251.73 162.44 0.1774E+03 0.1326E+03 0.1599E+03 0.1707E+03 9 1.42 320.78 285.71 319.78 241.69 0.1395E+03 0.9412E+02 0.1365E+03 0.1698E+03 11 1.98 390.15 331.03 392.35 335.89 0.1310E+03 0.7016E+02 0.1233E+03 0.1659E+03 13 2.54 467.40 366.07 457.88 426.27 0.1149E+03 0.5625E+02 0.1107E+03 0.1561E+03 15 3.19 524.96 399.31 525.19 521.99 0.9116E+02 0.4587E+02 0.9441E+02 0.1339E+03 17 4.47 619.60 449.77 626.53 654.05 0.5999E+02 0.3404E+02 0.6472E+02 0.7150E+02 19 5.88 691.39 492.20 699.77 718.44 0.4275E+02 0.2677E+02 0.4052E+02 0.2613E+02 21 7.86 760.86 538.71 755.65 745.76 0.2548E+02 0.2079E+02 0.1764E+02 0.6373E+01 23 10.05 795.67 579.49 788.94 753.35 0.9508E+01 0.1681E+02 0.1815E+02 0.1712E+01 25 11.80 813.12 606.87 814.25 755.32 0.1042E+02 0.1464E+02 0.1156E+02 0.7093E+00 27 14.03 829.02 637.23 835.78 756.33 0.3013E+01 0.1261E+02 0.8473E+01 0.2710E+00 29 16.18 845.71 662.63 853.81 756.72 0.1328E+02 0.1117E+02 0.8705E+01 0.1229E+00 31 18.73 879.76 689.36 878.13 756.94 0.1231E+02 0.9860E+01 0.1048E+02 0.5434E-01 33 21.24 908.29 712.88 906.93 757.03 0.1249E+02 0.8857E+01 0.1234E+02 0.2687E-01 35 23.20 934.42 729.53 932.19 757.08 0.1767E+02 0.8220E+01 0.1349E+02 0.1645E-01 37 25.24 967.25 745.75 960.75 757.10 0.1154E+02 0.7653E+01 0.1438E+02 0.1026E-01 39 27.32 992.21 761.12 991.30 757.12 0.1258E+02 0.7158E+01 0.1499E+02 0.6596E-02 41 29.13 1017.93 773.89 1018.76 757.13 0.1600E+02 0.6775E+01 0.1534E+02 0.4610E-02 43 31.22 1042.89 787.64 1051.17 757.14 0.9048E+01 0.6391E+01 0.1560E+02 0.3128E-02 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 30



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 3 ts = 0.5000" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 1/2 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 31


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.10384737E+05

-9






A.3 – 32



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 3 ts = 0.6250" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 5/8 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 33


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.12884213E+05

-9






A.3 – 34



1) 2)


1

ta = 0.2500" cl = 1.2500" nc = 1 X 3 ts = 0.5000" gs’= 2.5000" rs = 5.5000"

------------------------------


2

= 2.8125" = 1.2500" = 1 X 3 = 8.0000" = 3.5000" = 3.5000"

ns = 2 X

ll cu nb ls gs qs


= 8.5000" = 2.0000" = 3.0000" = 8.0000" = 3.5000" = 3.5000" = 2.5000" = 2 X 2

Major parameters

X 8.0 X 8.5

U.S.A.



W12X96 W14X38 6 X 4.0 X 1/2 4 X 3.5 X 1/4

: :


Remark



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 35


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.21081811E+05

-9






A.3 – 36



1) 2)

8.0000" 5.5000"

2.8125" 1.2500" ts = rs =

ta = pc = 0.3750" 5.5000"

0.2500" 3.0000"

------------------------------



ls = rt =

tt = 0.3750" gs’= 2.5000" ns’= 2 X 1


Remark

ll = cl =

2.8125" 1.2500"

lu = cu =

Major parameters

X 8.0 X 8.5

U.S.A.


A.Azizinamini et al. (1985) 14WS1

W12X96 W14X38 6 X 4.0 X 3/8 4 X 3.5 X 1/4

: :

lp = 8.5000" gc = 2.5940" nc = 1 X 3 lt = 8.0000" gt’= 2.5000" nt’= 2 X 1


Tested by Test Id.

III - 19 Connection type : Top-and seat-angle connections with double web angle Mode : Welded-to-beam and bolted-to-column

Moment ( kip-inch )

0

150

300

450

600

750

900

1050

1200

1350

1500

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 37


R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.90695243E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3221E+04 0.3856E+03 0.7504E+03 0.1448E+03 3 0.02 76.03 9.06 17.01 3.40 0.3235E+04 0.3845E+03 0.6975E+03 0.1448E+03 5 0.28 142.00 97.37 139.33 40.52 0.1143E+03 0.2899E+03 0.3069E+03 0.1448E+03 7 0.83 208.53 208.38 222.06 120.02 0.1278E+03 0.1427E+03 0.7464E+02 0.1444E+03 9 1.66 295.96 294.69 284.39 238.46 0.8353E+02 0.7877E+02 0.8953E+02 0.1410E+03 11 2.47 365.68 348.16 362.92 349.75 0.1043E+03 0.5525E+02 0.9610E+02 0.1303E+03 13 3.12 417.68 380.35 420.82 429.48 0.6420E+02 0.4496E+02 0.8149E+02 0.1151E+03 15 4.22 489.02 423.41 495.24 537.63 0.5989E+02 0.3444E+02 0.5594E+02 0.8106E+02 17 5.92 577.36 473.79 574.62 634.78 0.4681E+02 0.2556E+02 0.4102E+02 0.3675E+02 19 8.01 660.26 520.34 654.18 682.12 0.3114E+02 0.1965E+02 0.3506E+02 0.1291E+02 21 9.66 705.34 550.26 706.31 697.00 0.2476E+02 0.1670E+02 0.2755E+02 0.6059E+01 23 11.26 740.97 575.16 743.64 704.06 0.2112E+02 0.1464E+02 0.1935E+02 0.3165E+01 25 12.85 772.67 597.20 768.68 707.87 0.1801E+02 0.1306E+02 0.2253E+02 0.1774E+01 27 14.82 803.64 621.41 806.66 710.44 0.1487E+02 0.1156E+02 0.1649E+02 0.9415E+00 29 17.11 835.44 646.25 839.45 712.02 0.1348E+02 0.1023E+02 0.1267E+02 0.4949E+00 31 19.18 862.49 666.38 863.78 712.82 0.1293E+02 0.9280E+01 0.1108E+02 0.2959E+00 33 21.58 890.38 687.68 889.32 713.36 0.1002E+02 0.8390E+01 0.1036E+02 0.1737E+00 35 23.35 911.88 701.99 907.48 713.62 0.1464E+02 0.7849E+01 0.1018E+02 0.1215E+00 37 25.63 940.54 719.15 930.68 713.85 0.7192E+01 0.7255E+01 0.1013E+02 0.7948E-01 39 27.33 948.66 731.27 947.86 713.96 0.5495E+01 0.6868E+01 0.1014E+02 0.5942E-01 41 29.71 965.93 747.01 972.05 714.08 0.8093E+01 0.6402E+01 0.1016E+02 0.4063E-01 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 38



1) 2)

8.0000" 5.5000"

2.8125" 1.2500" ts = rs =

ta = pc = 0.5000" 5.5000"

0.2500" 3.0000"

------------------------------



ls = rt =

tt = 0.5000" gs’= 2.5000" ns’= 2 X 1


Remark

ll = cl =

2.8125" 1.2500"

lu = cu =

Major parameters

X 8.0 X 8.5

U.S.A.


A.Azizinamini et al. (1985) 14WS2

W12X96 W14X38 6 X 4.0 X 1/2 4 X 3.5 X 1/4

: :

lp = 8.5000" gc = 2.5940" nc = 1 X 3 lt = 8.0000" gt’= 2.5000" nt’= 2 X 1


Tested by Test Id.

III - 20 Connection type : Top-and seat-angle connections with double web angle Mode : Welded-to-beam and bolted-to-column

Moment ( kip-inch )

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

gb

ta

column

5

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

20

25

30

35

40

45


ll

lp

lu beam

gt'


10

gs

gt

50

ts

tt

A.3 – 39


R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.62342746E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1706E+04 0.5334E+03 0.8630E+03 0.3527E+03 3 0.07 113.98 35.32 53.40 23.51 0.1395E+04 0.5220E+03 0.7417E+03 0.3520E+03 5 0.30 179.25 143.58 190.45 105.58 0.3340E+03 0.3875E+03 0.4526E+03 0.3434E+03 7 0.50 256.30 210.88 266.85 173.51 0.3701E+03 0.2883E+03 0.3193E+03 0.3309E+03 9 0.71 328.64 262.32 323.24 238.97 0.3071E+03 0.2246E+03 0.2451E+03 0.3151E+03 11 1.22 420.68 353.22 426.73 388.51 0.1932E+03 0.1426E+03 0.1761E+03 0.2682E+03 13 1.67 512.71 408.81 501.21 499.39 0.1768E+03 0.1084E+03 0.1574E+03 0.2260E+03 15 2.21 590.60 460.90 582.06 610.03 0.1288E+03 0.8429E+02 0.1379E+03 0.1800E+03 17 3.15 682.31 528.05 693.49 748.69 0.9094E+02 0.6166E+02 0.1003E+03 0.1203E+03 19 4.30 785.84 589.77 787.26 858.72 0.8010E+02 0.4681E+02 0.6547E+02 0.7469E+02 21 6.16 890.65 663.73 882.68 958.60 0.4176E+02 0.3415E+02 0.4497E+02 0.3787E+02 23 8.42 968.81 730.79 970.68 1019.91 0.3091E+02 0.2603E+02 0.3374E+02 0.1915E+02 25 10.26 1019.39 774.72 1025.47 1047.95 0.2403E+02 0.2193E+02 0.2580E+02 0.1203E+02 27 12.25 1067.24 814.99 1068.81 1067.22 0.2420E+02 0.1884E+02 0.1817E+02 0.7810E+01 29 14.20 1108.01 849.50 1104.24 1079.92 0.1690E+02 0.1659E+02 0.1900E+02 0.5388E+01 31 15.86 1135.77 875.74 1132.81 1087.69 0.1655E+02 0.1510E+02 0.1566E+02 0.4066E+01 33 17.62 1156.08 901.05 1158.08 1093.93 0.7709E+01 0.1380E+02 0.1332E+02 0.3103E+01 35 19.48 1176.80 925.92 1181.36 1099.01 0.1494E+02 0.1266E+02 0.1178E+02 0.2389E+01 37 21.22 1198.67 947.12 1201.04 1102.73 0.1018E+02 0.1177E+02 0.1092E+02 0.1910E+01 39 22.89 1218.97 966.19 1218.90 1105.62 0.1415E+02 0.1104E+02 0.1043E+02 0.1564E+01 41 24.51 1240.04 983.47 1235.46 1107.93 0.1196E+02 0.1042E+02 0.1014E+02 0.1306E+01 43 26.28 1256.03 1001.28 1253.24 1110.04 0.6616E+01 0.9828E+01 0.9949E+01 0.1086E+01 45 28.54 1269.73 1022.71 1275.55 1112.24 0.5650E+01 0.9166E+01 0.9822E+01 0.8718E+00 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 40


: :

J.C.Rathbun (1936) B-11


1) 2)

lu = 1.5000" gc = 2.2500" pc = 3.0000" tt = 0.3750" gt’= 3.7500" rt = 5.5000" pt’= 2.5000" nt’= 2 X 2

ll cu nb ls gs qs ps ns

= 1.5900" = 1.5000" = 1 X 3 = 9.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2 ns’= 2 X

------------------------------


1

ta = 0.3750" cl = 1.5000" nc = 1 X 3 ts = 0.3750" gs’= 2.5000" rs = 5.5000"

6 X 4.0 X 3/8 X 9 ( SEAT ) Connection cleat riveted to 1" mounting plate.

= 9.0000" = 2.2500" = 3.0000" = 9.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2


Remark


U.S.A. Fasteners: 10.9- -7/8"D 15/16" Oversize holes Material : -Fy = 47.12 ksi Fu = 62.90 ksi

Major parameters

Column : -Beam : W12X31.8 F.Angle: 6 X 6.0 X 3/8 X 9 ( TOP ) W.Angle: 4 X 3.5 X 3/8 X 9

Tested by Test Id.

III - 21 Connection type : Top-and seat-angle connections with double web angle Mode : All riveted

0 0.0

70

140

210

280

350

420

490

560

630

700

0.9

gb

ta

column

pt

2.7

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

3.6

4.5

5.4

6.3

7.2

8.1


ll

lp

lu beam

gt'


1.8

gs

gt

9.0

ts

tt

A.3 – 41


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.31791970E+03

-9



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.65654167E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.13030326E+03 -0.12243151E+04 0.57311383E+04 -0.10463346E+05 0.65761576E+04 Rj0 = 2.8100 5.1600 RKj = 0.38285972E+02 -0.11044250E+02



A.3 – 42


: :



1) 2)

lu = 1.5000" gc = 2.2500" pc = 3.0000" tt = 0.3750" gt’= 3.7500" rt = 5.5000" rs = 5.5000" pt’= 2.5000" nt’= 4 X 2

ll = 1.5900" cu = 1.5000" nb = 1 X 3 ls = 14.0000" gs = 3.5000" rt2= 2.5000" rs2= 2.5000" ps = 2.5000" ns = 2 X 2 ns’= 4 X

------------------------------


1

ta = 0.3750" cl = 1.5000" nc = 1 X 3 ts = 0.3750" gs’= 2.5000"

6 X 4.0 X 3/8 X 14 ( SEAT ) Connection cleat riveted to 1" mounting plate.

= 9.0000" = 2.2500" = 3.0000" = 14.0000" = 3.5000" = 2.7500" = 2.7500" = 2.5000" = 2 X 2


Remark

lp gb pb lt gt qt qs pt nt

U.S.A. Fasteners: 10.9- -7/8"D 15/16" Oversize holes Material : -Fy = 47.12 ksi Fu = 62.90 ksi

Major parameters

Column : -Beam : W12X31.8 F.Angle: 6 X 6.0 X 3/8 X 14 ( TOP ) W.Angle: 4 X 3.5 X 3/8 X 9

Tested by Test Id.

III - 22 Connection type : Top-and seat-angle connections with double web angle Mode : All riveted

0

95

190

285

380

475

570

665

760

855

950

0

2

gb

ta

column

pt

6

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

8

10

12

14

16

18


ll

lp

lu beam

gt'


4

gs

gt

20

ts

tt

A.3 – 43


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.30070293E+05

-9






A.3 – 44



Remark


1) 2)

ns’= 2 X

1

ta = 0.3125" cl = 2.0000" nc = 1 X 4 ts = 0.6250" gs’= 2.0000" rs = -"

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 53.05 0.28 3 107.13 0.86 4 151.40 1.52 5 188.83 2.41 6 223.33 3.37 7 262.76 4.47 8 312.95 5.30 9 358.22 6.14 10 403.53 7.16 11 437.05 8.15 12 470.60 9.32 13 496.33 10.72 14 525.03 12.28 15 551.77 13.93 16 569.62 15.15 17 590.45 16.58 18 609.32 18.06 19 625.25 19.59 20 640.22 21.25 21 650.27 22.88 22 659.45 25.20 23 662.66 26.98 ------------------------------

Fy = 289.8 MPa, Fu = 441.6 MPa for top- and seat angle

2

= 1.8701" = 2.0000" = 1 X 4 = 5.5118" = 3.0000" = -"

ns = 2 X

ll cu nb ls gs qs

Major parameters

lu = 1.8701" gc = -" pc = 2.0000" tt = 0.6250" gt’= 2.0000" rt = -" ps = 2.0000" nt’= 2 X 1

U.S.A.


C.W. Roeder et al. (1996) L1

W10x68 W14x22 L5x3.5x5/8 L3.5x3x5/16

: :

= 10.0000" = -" = 2.0000" = 5.5118" = 3.0000" = -" = 2.0000" = 2 X 2


Tested by Test Id.


Moment ( kip-inch )

0

80

160

240

320

400

480

560

640

720

800

0

5

gb

ta

column

pt

15

pb cl ps

cu pb

gs'

pc

pc

gc

20

25

30

35

40


ll

lp

lu beam

gt'


10

gs

gt

qs

qt

45

rs ls

lt rt

50

ts

tt

A.3 – 45


R tc A3 P3


( R : X 1/1000 radians )

Q3 =


-9





A.3 – 46



1) 2)

lu = 1.1811" gc = -" pc = -" tt = 0.3543" gt’= 1.5748" rt = -" ps = 0.0000" nt’= 2 X 1 ns’= 2 X

1

------------------------------

gb

ta

column


ta = 0.3150" cl = 0.9842" nc = 1 X 3 ts = 0.3543" gs’= 1.5748" rs = -"


2

= 1.1811" = 0.9842" = 1 X 3 = 5.9055" = 1.5748" = -"

ns = 2 X

ll cu nb ls gs qs

Major parameters

column stiffener (thickness 9 mm)

= 7.4803" = -" = 2.7559" = 5.9055" = 1.5748" = -" = 0.0000" = 2 X 2

U.K.

Fasteners: 10.9- -M16 23/32" Oversize holes Material : -Fy = 44.96 ksi Fu = 65.27 ksi

A.S. Elnashai et al. (1998) SRB01

H150x150x7x10 H250x130x9x9 L75x75x9 L75x75x8

: :


Remark



Tested by Test Id.


Moment ( kip-inch )

0

85

170

255

340

425

510

595

680

765

850

0

gs

gt

24

pt

72

ll

lp

gs'

pc

pc

gc

96

rs ls

qs

qt

ts

tt

120 144 168 192 216 240


lu beam


48

pb cl ps

cu pb

gt'

lt rt

A.3 – 47


R tc A3 P3


( R : X 1/1000 radians )

Q3 =


-9

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1262E+03 0.4102E+03 0.1587E+03 3 0.49 61.78 159.00 70.53 0.1262E+03 0.2261E+03 0.1303E+03 5 1.00 126.21 245.61 130.51 0.1262E+03 0.1299E+03 0.1055E+03 7 1.74 199.70 320.72 197.75 0.7687E+02 0.8005E+02 0.7652E+02 9 2.54 251.34 374.41 248.99 0.4597E+02 0.5735E+02 0.5318E+02 11 3.68 301.42 429.39 295.33 0.3560E+02 0.4135E+02 0.3014E+02 13 6.16 326.39 510.25 334.24 0.4716E+01 0.2629E+02 0.5682E+01 15 12.19 331.48 626.01 332.79 0.1710E+01 0.1454E+02 -0.7401E+00 17 16.94 347.25 685.62 336.85 0.2619E+01 0.1097E+02 0.2267E+01 19 21.84 355.42 733.74 351.72 0.2802E+01 0.8841E+01 0.3479E+01 21 27.72 367.35 780.64 372.18 0.2541E+01 0.7224E+01 0.3357E+01 23 33.77 380.79 820.77 391.66 0.2409E+01 0.6117E+01 0.3154E+01 25 39.33 399.57 852.67 409.67 0.4447E+01 0.5381E+01 0.3379E+01 27 44.42 428.24 878.68 427.93 0.5990E+01 0.4859E+01 0.3811E+01 29 48.53 455.43 897.92 444.36 0.5916E+01 0.4512E+01 0.4177E+01 31 54.11 481.81 921.95 468.77 0.4530E+01 0.4120E+01 0.4548E+01 33 60.17 504.37 945.82 496.91 0.3408E+01 0.3771E+01 0.4692E+01 35 66.88 527.66 970.19 528.04 0.3080E+01 0.3451E+01 0.4531E+01 37 71.80 547.22 986.57 549.65 0.8270E+01 0.3254E+01 0.4246E+01 39 75.58 573.67 998.76 565.20 0.4278E+01 0.3117E+01 0.3963E+01 41 81.95 586.34 1017.95 588.74 0.1485E+01 0.2914E+01 0.3417E+01 43 89.95 595.15 1040.41 613.21 0.1171E+01 0.2697E+01 0.2707E+01 45 96.81 611.60 1058.25 629.83 0.3492E+01 0.2539E+01 0.2144E+01 47 103.84 626.53 1075.50 643.09 0.1934E+01 0.2397E+01 0.1647E+01 49 111.36 642.19 1093.00 653.78 0.1551E+01 0.2262E+01 0.1213E+01 51 120.17 654.77 1112.32 662.67 0.1405E+01 0.2124E+01 0.8259E+00 53 129.32 669.62 1131.15 668.84 0.1526E+01 0.1999E+01 0.5418E+00 55 137.64 678.42 1147.57 672.56 0.9567E+00 0.1898E+01 0.3630E+00 57 145.80 686.46 1162.58 675.00 0.8301E+00 0.1810E+01 0.2421E+00 59 153.30 693.01 1176.02 676.51 0.9742E+00 0.1736E+01 0.1652E+00 61 159.66 699.61 1186.70 677.41 0.1126E+01 0.1680E+01 0.1187E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.13939892E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = 0.27365324E+03 0.65456079E+04 -0.41423927E+05 0.10433520E+06 -0.11614065E+06



A.3 – 48



1) 2)

lu = 0.9843" gc = 1.7716" pc = 2.5591" tt = 0.3347" gt’= 1.7716" rt = 2.9528" nt’= 2 X 1

ll cu nb ls gs qs ns

= 0.9843" = 1.3780" = 1 X 3 = 5.1181" = 1.8701" = 2.9528" = 2 X 1

ta = 0.3347" cl = 1.3780" nc = 1 X 3 ts = 0.3347" gs’= 1.7716" rs = 2.9528" ns’= 2 X 1

------------------------------


Beam was applied to 49 kN of compressive axial force

= 7.8740" = 1.8701" = 2.5591" = 5.1181" = 1.8701" = 2.9528" = 2 X 1

Japan Fasteners: F10T- -M16 23/32" Oversize holes Material : SS400 Fy = -ksi Fu = -ksi

Major parameters

Z. Fu et al. (1998) LM-P

-H250x125x6x9 L75x75x9x8.5 L75x75x9x8.5

: :


Remark

lp gb pb lt gt qt nt


Tested by Test Id.


Moment ( kip-inch )

0

85

170

255

340

425

510

595

680

765

850

0

13

gb

ta

column

pt

39

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

52

65

78

91

ts

tt

104 117 130

Material : SS400 Fy = 34.08 ksi (nominal) : Experimental : Polynominal : M. Exponential : Power model, n = 1.14

ll

lp

lu beam

gt'


26

gs

gt

A.3 – 49


R tc A3 P3



0.13817269E+06

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1207E+03 0.2936E+03 0.9812E+02 0.1918E+03 3 0.84 80.86 159.85 76.38 128.64 0.7204E+02 0.1074E+03 0.8288E+02 0.1184E+03 5 2.17 161.41 251.58 169.41 241.03 0.6686E+02 0.4722E+02 0.5803E+02 0.5955E+02 7 4.02 253.72 317.02 254.38 317.90 0.3572E+02 0.2735E+02 0.3622E+02 0.2877E+02 9 6.91 332.25 378.70 332.19 373.40 0.1965E+02 0.1700E+02 0.1937E+02 0.1273E+02 11 11.42 375.33 439.72 379.77 410.64 0.3910E+01 0.1100E+02 0.3314E+01 0.5323E+01 13 17.19 382.99 492.61 383.55 431.60 0.3733E+01 0.7754E+01 0.1815E+01 0.2467E+01 15 21.48 406.43 522.79 409.59 440.12 -0.2387E+03 0.6416E+01 0.1094E+02 0.1597E+01 17 22.51 374.94 529.35 371.66 441.69 0.2712E+02 0.6162E+01 0.2730E+02 0.1455E+01 19 25.40 410.22 546.19 405.78 445.42 0.6942E+01 0.5566E+01 0.3125E+01 0.1144E+01 21 29.91 436.60 569.59 435.33 449.79 0.4705E+01 0.4848E+01 0.9128E+01 0.8234E+00 23 34.65 460.02 591.17 464.75 453.16 0.6911E+01 0.4283E+01 0.6352E+01 0.6106E+00 25 39.53 491.30 610.93 490.16 455.76 0.4229E+01 0.3834E+01 0.3595E+01 0.4662E+00 27 44.63 519.62 629.50 518.59 457.86 -0.4298E+01 0.3463E+01 0.7544E+01 0.3631E+00 29 47.44 513.62 639.11 508.12 458.82 0.1081E+02 0.3288E+01 0.7113E+01 0.3200E+00 31 50.84 526.28 649.92 526.87 459.83 -0.3352E+02 0.3105E+01 0.3968E+01 0.2773E+00 33 51.95 475.13 653.35 486.26 460.13 -0.1563E+02 0.3049E+01 -0.3706E+02 0.2651E+00 35 54.10 528.13 659.85 516.52 460.68 0.1794E+02 0.2946E+01 0.1323E+02 0.2437E+00 37 58.24 569.26 671.63 565.20 461.61 0.8124E+01 0.2771E+01 0.1040E+02 0.2090E+00 39 62.16 602.54 682.18 601.68 462.38 0.9728E+01 0.2625E+01 0.8302E+01 0.1824E+00 41 66.97 634.80 694.37 636.76 463.19 0.7563E+01 0.2468E+01 0.6398E+01 0.1561E+00 43 71.11 662.17 704.46 660.71 463.80 0.4915E+01 0.2346E+01 0.5234E+01 0.1377E+00 45 76.14 683.62 715.89 684.42 464.44 0.4613E+01 0.2217E+01 0.4262E+01 0.1193E+00 47 80.28 699.20 724.79 700.89 464.91 0.1369E+01 0.2123E+01 0.3725E+01 0.1067E+00 ----------------------------------------------------------------------------------------------------------------------------


Q3 =

) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 0.00000000E+00 Nexp= 6 Nliner= 9 -0.97196347E+05 0.27814927E+06 -0.33051229E+06 23.6200 29.9100 42.1200 50.8400 51.9500 -0.30383615E+02 -0.38573329E+01 0.86825301E+01 -0.40076114E+02 0.52009854E+02


( R : X 1/1000 radians )

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) C = 0.74900000E+00 Bmo= AI = -0.42443152E+03 0.13013118E+05 Rj0 = 21.4800 21.7000 44.6300 46.6300 RKj = -0.28059621E+03 0.29449691E+03 -0.14831602E+02 0.17156619E+02



A.3 – 50



1) 2)



= 0.9843" = 1.3780" = 1 X 3 = 5.1181" = 1.8701" = 2.9528" = 2 X 1


------------------------------

gb

ta

column



Beam was applied to 49 kN of tensile axial force

= 7.8740" = 1.8701" = 2.5591" = 5.1181" = 1.8701" = 2.9528" = 2 X 1


Major parameters

Z. Fu et al. (1998) LM-T

-H250x125x6x9 L75x75x9x8.5 L75x75x9x8.5

: :


Remark



Tested by Test Id.


Moment ( kip-inch )

0

85

170

255

340

425

510

595

680

765

850

0

gs

gt

12

pt

36

ll

lp

gs'

pc

pc

gc

rs ls

qs

qt

48

60

72

84

96

ts

tt

108 120


lu beam


24

pb cl ps

cu pb

gt'

lt rt

A.3 – 51


R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.21298244E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.9470E+02 0.2936E+03 0.1034E+03 0.1918E+03 3 0.92 80.86 168.07 81.60 136.90 0.7392E+02 0.9969E+02 0.7696E+02 0.1119E+03 5 1.88 148.64 237.02 147.60 220.58 0.7082E+02 0.5361E+02 0.6173E+02 0.6751E+02 7 3.06 223.29 287.50 212.38 282.44 0.6005E+02 0.3481E+02 0.4858E+02 0.4055E+02 9 5.28 293.98 347.52 296.99 344.99 0.3162E+02 0.2152E+02 0.2841E+02 0.1947E+02 11 8.02 347.93 396.31 349.53 383.33 0.1261E+02 0.1494E+02 0.1176E+02 0.1002E+02 13 12.08 379.24 446.77 378.01 411.79 0.3810E+01 0.1049E+02 0.5121E+01 0.4887E+01 15 16.82 383.99 489.70 386.13 428.83 0.2123E+01 0.7900E+01 0.2816E+01 0.2637E+01 17 21.11 405.46 520.40 403.71 437.92 0.4798E+01 0.6511E+01 0.4845E+01 0.1701E+01 19 25.03 421.04 544.11 421.83 443.56 0.3449E+01 0.5636E+01 0.4052E+01 0.1218E+01 21 29.76 433.65 568.86 434.89 448.41 0.6838E+01 0.4869E+01 0.1310E+01 0.8626E+00 23 33.91 463.97 587.97 459.14 451.55 0.4225E+01 0.4362E+01 0.4568E+01 0.6635E+00 25 36.20 444.24 597.69 456.62 452.97 -0.1062E+03 0.4128E+01 -0.4905E+02 0.5813E+00 27 37.68 441.24 603.74 433.05 453.80 0.3051E+02 0.3990E+01 0.1720E+02 0.5360E+00 29 40.05 472.60 612.91 472.67 454.99 0.6449E+01 0.3792E+01 0.1627E+02 0.4735E+00 31 41.89 471.56 619.82 480.50 455.83 -0.2349E+01 0.3651E+01 0.3977E+01 0.4320E+00 33 44.85 492.09 630.30 491.18 457.02 -0.3975E+01 0.3448E+01 0.3287E+01 0.3758E+00 35 46.70 499.89 636.63 496.97 457.69 0.1278E+02 0.3333E+01 0.2983E+01 0.3459E+00 37 48.48 476.24 642.52 480.57 458.28 0.1316E+02 0.3229E+01 -0.1531E+02 0.3204E+00 39 50.18 511.56 647.79 509.25 458.80 0.1059E+02 0.3140E+01 0.1680E+02 0.2985E+00 41 52.10 509.53 653.77 520.35 459.36 -0.5743E+01 0.3042E+01 0.5725E+01 0.2763E+00 43 55.36 541.84 663.40 538.83 460.20 0.6234E+01 0.2892E+01 0.5630E+01 0.2438E+00 45 59.43 564.30 674.82 561.70 461.12 0.5969E+01 0.2726E+01 0.5624E+01 0.2106E+00 47 64.23 586.74 687.49 588.85 462.06 0.5075E+01 0.2555E+01 0.5695E+01 0.1794E+00 49 67.93 615.11 696.84 610.05 462.68 0.8139E+01 0.2437E+01 0.5769E+01 0.1597E+00 51 71.93 633.64 706.29 633.29 463.28 0.6325E+01 0.2325E+01 0.5848E+01 0.1418E+00 53 75.92 659.06 715.46 656.76 463.82 0.6200E+01 0.2222E+01 0.5918E+01 0.1268E+00 55 79.92 680.54 724.07 680.56 464.30 0.5635E+01 0.2130E+01 0.5975E+01 0.1139E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.78350000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.39357637E+03 -0.74896626E+04 0.39521954E+05 -0.79971608E+05 0.69409910E+05 Rj0 = 12.8000 29.7600 35.9800 36.9400 40.0500 47.2900 48.4800 50.1800 RKj = -0.57802723E+01 0.58556178E+01 -0.52378811E+02 0.66939980E+02 -0.11716399E+02 -0.18072969E+02 0.32259309E+02 -0.10962812E+02



A.3 – 52



1) 2)



= 0.9843" = 1.3780" = 1 X 3 = 5.1181" = 1.8701" = 2.9528" = 2 X 1


------------------------------


Beam was applied to 147 kN of compressive axial force

= 7.8740" = 1.8701" = 2.5591" = 5.1181" = 1.8701" = 2.9528" = 2 X 1


Major parameters

Z. Fu et al. (1998) LM-P15

-H250x125x6x9 L75x75x9x8.5 L75x75x9x8.5

: :


Remark



Tested by Test Id.


Moment ( kip-inch )

0

85

170

255

340

425

510

595

680

765

850

0

12

gb

ta

column

pt

36

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

48

60

72

84

96

ts

tt

108 120


ll

lp

lu beam

gt'


24

gs

gt

A.3 – 53


R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.36391486E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.7443E+02 0.2936E+03 0.8519E+02 0.1918E+03 3 0.77 73.00 151.99 62.53 109.66 0.9714E+02 0.1154E+03 0.7518E+02 0.1071E+03 5 2.76 173.18 276.56 172.51 241.77 0.4592E+02 0.3815E+02 0.3785E+02 0.4142E+02 7 5.87 256.61 359.65 256.57 323.53 0.2113E+02 0.1961E+02 0.2351E+02 0.1674E+02 9 9.79 286.94 420.49 282.37 368.71 -0.1453E+01 0.1257E+02 0.5482E+00 0.7950E+01 11 14.08 275.97 466.38 275.50 394.22 0.5536E+01 0.9197E+01 -0.5233E+01 0.4452E+01 13 17.48 261.11 494.82 256.34 406.85 -0.4997E+01 0.7645E+01 -0.2102E+02 0.3102E+01 15 22.22 319.91 527.47 324.26 418.81 0.1373E+02 0.6234E+01 0.1148E+02 0.2053E+01 17 27.62 381.64 558.11 377.69 427.97 0.8924E+01 0.5185E+01 0.8911E+01 0.1400E+01 19 32.87 427.65 583.37 422.79 434.25 0.8760E+01 0.4478E+01 0.8387E+01 0.1025E+01 21 37.38 463.85 602.63 459.97 438.37 0.6798E+01 0.4015E+01 0.8070E+01 0.8119E+00 23 42.93 493.14 623.52 503.01 442.34 0.6955E+01 0.3578E+01 0.7390E+01 0.6304E+00 25 49.29 537.14 644.98 546.83 445.87 0.6704E+01 0.3187E+01 0.6373E+01 0.4887E+00 27 55.28 580.18 663.16 582.19 448.50 0.7145E+01 0.2896E+01 0.5459E+01 0.3950E+00 29 60.54 615.37 677.83 609.13 450.41 0.5642E+01 0.2684E+01 0.4811E+01 0.3334E+00 31 65.64 641.73 691.06 632.40 451.98 0.3934E+01 0.2509E+01 0.4340E+01 0.2866E+00 33 68.89 651.44 699.13 646.12 452.87 0.3108E+01 0.2410E+01 0.4113E+01 0.2618E+00 35 72.81 661.13 708.28 661.81 453.85 0.1986E+01 0.2302E+01 0.3902E+01 0.2359E+00 37 75.62 665.95 714.70 672.61 454.49 0.1297E+01 0.2230E+01 0.3786E+01 0.2197E+00 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 54



1) 2)



= 0.9843" = 1.3780" = 1 X 3 = 5.1181" = 1.8701" = 2.9528" = 2 X 1


------------------------------


Beam was applied to 147 kN of tensile axial force

= 7.8740" = 1.8701" = 2.5591" = 5.1181" = 1.8701" = 2.9528" = 2 X 1


Major parameters

Z. Fu et al. (1998) LM-T15

-H250x125x6x9 L75x75x9x8.5 L75x75x9x8.5

: :


Remark



Tested by Test Id.


Moment ( kip-inch )

0

85

170

255

340

425

510

595

680

765

850

0

12

gb

ta

column

pt

36

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

48

60

72

84

96

ts

tt

108 120


ll

lp

lu beam

gt'


24

gs

gt

A.3 – 55


R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.89014554E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.8628E+02 0.2936E+03 0.8810E+02 0.1918E+03 3 1.06 87.73 181.21 87.14 150.04 0.7541E+02 0.8844E+02 0.7552E+02 0.1014E+03 5 2.39 170.24 261.53 175.12 247.55 0.6324E+02 0.4334E+02 0.5676E+02 0.5265E+02 7 4.02 247.83 317.11 250.36 310.81 0.3588E+02 0.2733E+02 0.3638E+02 0.2851E+02 9 6.02 304.76 362.54 304.15 353.60 0.1900E+02 0.1918E+02 0.1880E+02 0.1602E+02 11 9.20 305.63 412.89 312.37 389.81 -0.5461E+01 0.1327E+02 -0.1171E+02 0.8072E+01 13 11.05 335.05 435.52 328.40 402.56 0.2141E+02 0.1133E+02 0.1990E+02 0.5879E+01 15 15.86 381.07 481.94 380.46 422.97 0.5925E+01 0.8306E+01 0.5257E+01 0.3056E+01 17 21.41 410.36 522.34 412.61 435.75 0.6587E+01 0.6433E+01 0.6047E+01 0.1733E+01 19 26.07 440.66 549.88 440.21 442.43 0.5774E+01 0.5445E+01 0.5716E+01 0.1184E+01 21 31.24 468.98 575.92 468.09 447.56 0.4577E+01 0.4674E+01 0.5067E+01 0.8298E+00 23 36.72 495.33 599.82 494.28 451.43 0.4337E+01 0.4079E+01 0.4540E+01 0.6019E+00 25 42.56 519.69 622.19 519.96 454.46 0.5066E+01 0.3604E+01 0.4304E+01 0.4479E+00 27 48.55 546.01 642.60 545.67 456.81 0.4191E+01 0.3228E+01 0.4312E+01 0.3435E+00 29 53.36 565.50 657.52 566.62 458.32 0.4810E+01 0.2983E+01 0.4405E+01 0.2837E+00 31 58.32 586.95 671.77 588.76 459.60 0.4134E+01 0.2769E+01 0.4524E+01 0.2368E+00 33 63.42 613.30 685.41 612.14 460.71 0.4097E+01 0.2582E+01 0.4639E+01 0.1996E+00 35 66.60 627.93 693.54 626.99 461.31 -0.9206E+00 0.2478E+01 0.4700E+01 0.1806E+00 37 68.82 631.79 699.01 628.29 461.70 0.1000E+02 0.2411E+01 0.4896E+01 0.1689E+00 39 73.85 652.25 710.75 653.10 462.49 0.4821E+01 0.2274E+01 0.4965E+01 0.1462E+00 41 78.07 672.74 720.05 674.14 463.07 0.4112E+01 0.2172E+01 0.5007E+01 0.1305E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.78808333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.30849962E+02 -0.13314296E+04 0.10824861E+05 -0.24910686E+05 0.24691964E+05 Rj0 = 7.6500 9.8700 12.9700 17.4800 66.6000 67.7100 RKj = -0.16829168E+02 0.34613873E+02 -0.13273467E+02 0.44251293E+00 -0.84243210E+01 0.85826583E+01



A.3 – 56



1) 2)



= 1.1811" = 2.3622" = 1 X 3 = 5.9055" = 2.9528" = 3.1496" = 1.5748" = 2 X 2

ta = 0.3937" cl = 2.3622" nc = 1 X 3 ts = 0.3937" gs’= 2.9528" rs = 3.1496" ps’= 1.5748" ns’= 2 X 2

------------------------------


Continuity plate (12 mm in thickness) were used in column panel zone. Fybf=304.7, Fubf=452.6, Fybw=315.7, Fubw=452.6 N/mm2 for beam, Hole size:17mm

= 9.4488" = 2.9528" = 2.3622" = 5.9055" = 2.9528" = 3.1496" = 1.5748" = 2 X 2

Portugal Fasteners: G8.8- -M16 23/32" Oversize holes Material : S235 Fy = 36.58 ksi Fu = 60.94 ksi

Major parameters

L.Calado et al. (2000) BCC7-M

HEB200 IPE300 L120x120x10 L120x80x10

: :


Remark



Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

17

gb

ta

column

pt

51

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

68

85

ts

tt

102 119 136 153 170

Material : S235 Fy = 36.58 ksi : Experimental : Polynominal : M. Exponential : Power model, n = 1.01

ll

lp

lu beam

gt'


34

gs

gt

A.3 – 57


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.56214935E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2470E+03 0.2363E+03 0.3134E+03 0.3707E+03 3 0.49 124.14 91.64 134.52 151.46 0.2489E+03 0.1301E+03 0.2386E+03 0.2575E+03 5 1.03 247.62 143.73 245.27 268.78 0.2014E+03 0.7290E+02 0.1745E+03 0.1833E+03 7 2.00 373.84 195.78 372.92 407.53 0.1013E+03 0.4085E+02 0.9531E+02 0.1116E+03 9 3.99 463.02 254.48 474.20 560.45 0.2153E+02 0.2216E+02 0.2439E+02 0.5290E+02 11 11.98 542.07 358.70 528.25 747.95 0.7411E+01 0.8503E+01 0.9288E+01 0.1040E+02 13 19.96 607.32 412.67 612.59 801.22 0.1187E+02 0.5495E+01 0.9915E+01 0.4286E+01 15 27.95 689.87 450.55 685.24 826.42 0.9062E+01 0.4131E+01 0.8912E+01 0.2321E+01 17 35.93 758.76 480.13 761.76 841.07 0.9216E+01 0.3343E+01 0.1035E+02 0.1452E+01 19 43.92 839.07 504.64 848.30 850.67 0.1170E+02 0.2825E+01 0.1105E+02 0.9931E+00 21 51.90 939.13 525.64 934.32 857.43 0.1069E+02 0.2457E+01 0.1032E+02 0.7218E+00 23 59.89 1015.96 544.11 1011.16 862.45 0.8268E+01 0.2180E+01 0.8864E+01 0.5480E+00 25 67.87 1074.39 560.61 1075.87 866.33 0.6977E+01 0.1964E+01 0.7387E+01 0.4302E+00 27 75.86 1124.54 575.59 1129.92 869.41 0.5973E+01 0.1791E+01 0.6204E+01 0.3466E+00 29 83.84 1172.24 589.43 1175.90 871.92 0.5935E+01 0.1647E+01 0.5375E+01 0.2852E+00 31 91.83 1220.30 602.08 1216.54 874.00 0.5788E+01 0.1527E+01 0.4839E+01 0.2387E+00 33 99.81 1266.50 613.84 1253.74 875.76 0.4964E+01 0.1425E+01 0.4512E+01 0.2028E+00 35 107.80 1268.14 624.86 1288.95 877.26 -0.3726E+01 0.1338E+01 0.4321E+01 0.1744E+00 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 58



1) 2)



= 1.1811" = 2.3622" = 1 X 3 = 5.9055" = 2.9528" = 3.1496" = 1.5748" = 2 X 2


------------------------------



= 9.4488" = 2.9528" = 2.3622" = 5.9055" = 2.9528" = 3.1496" = 1.5748" = 2 X 2


Major parameters


HEB160 IPE300 L120x120x10 L120x80x10

: :


Remark



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

19

gb

ta

column

pt

57

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

76

95

ts

tt

114 133 152 171 190


ll

lp

lu beam

gt'


38

gs

gt

A.3 – 59


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.63662023E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1873E+03 0.2363E+03 0.2147E+03 0.3707E+03 3 0.93 168.59 136.06 169.72 246.66 0.1609E+03 0.7950E+02 0.1528E+03 0.1908E+03 5 2.21 337.17 203.98 322.79 423.38 0.9749E+02 0.3739E+02 0.9044E+02 0.1000E+03 7 4.25 421.47 260.08 441.70 565.44 0.2319E+02 0.2096E+02 0.3337E+02 0.4852E+02 9 9.17 509.80 331.96 495.60 703.59 0.1019E+02 0.1071E+02 0.3372E+01 0.1627E+02 11 15.29 540.42 384.01 543.52 769.07 0.8622E+01 0.6897E+01 0.1250E+02 0.7040E+01 13 21.40 622.32 420.34 630.36 801.16 0.1375E+02 0.5180E+01 0.1449E+02 0.3918E+01 15 27.52 705.88 448.76 711.44 820.28 0.1297E+02 0.4186E+01 0.1182E+02 0.2492E+01 17 33.63 780.06 472.22 776.09 832.95 0.1154E+02 0.3535E+01 0.9565E+01 0.1726E+01 19 39.75 844.67 492.36 831.01 841.99 0.8544E+01 0.3071E+01 0.8546E+01 0.1265E+01 21 45.86 888.68 510.02 881.75 848.75 0.6780E+01 0.2725E+01 0.8093E+01 0.9679E+00 23 51.98 927.46 525.83 929.90 854.02 0.6216E+01 0.2454E+01 0.7611E+01 0.7642E+00 25 58.09 964.53 540.14 974.32 858.22 0.6005E+01 0.2236E+01 0.6885E+01 0.6189E+00 27 64.21 1002.23 553.26 1013.67 861.66 0.6346E+01 0.2057E+01 0.5948E+01 0.5114E+00 29 70.32 1038.16 565.36 1046.90 864.53 0.5229E+01 0.1907E+01 0.4925E+01 0.4298E+00 31 76.44 1067.91 576.63 1073.95 866.95 0.4529E+01 0.1779E+01 0.3928E+01 0.3662E+00 33 82.55 1094.38 587.15 1095.17 869.03 0.3998E+01 0.1669E+01 0.3039E+01 0.3159E+00 35 88.67 1117.25 597.07 1111.40 870.84 0.3903E+01 0.1573E+01 0.2290E+01 0.2752E+00 37 94.78 1142.35 606.55 1123.49 872.41 0.4294E+01 0.1487E+01 0.1690E+01 0.2420E+00 39 100.90 1170.85 615.35 1132.34 873.81 0.4713E+01 0.1413E+01 0.1224E+01 0.2144E+00 41 108.00 1193.81 625.05 1139.54 875.23 -0.4274E+01 0.1336E+01 0.8265E+00 0.1880E+00 43 110.56 1059.41 628.46 1141.51 875.70 -0.2020E+03 0.1310E+01 0.7143E+00 0.1796E+00 45 116.18 1106.69 635.75 1144.94 876.67 0.8439E+01 0.1257E+01 0.5148E+00 0.1631E+00 47 122.30 1150.94 643.19 1147.58 877.62 0.2254E+01 0.1206E+01 0.3570E+00 0.1477E+00 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 60



1) 2)



= 1.1811" = 2.3622" = 1 X 3 = 5.9055" = 2.9528" = 3.1496" = 1.5748" = 2 X 2


------------------------------



= 9.4488" = 2.9528" = 2.3622" = 5.9055" = 2.9528" = 3.1496" = 1.5748" = 2 X 2


Major parameters


HEB240 IPE300 L120x120x10 L120x80x10

: :


Remark



Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

15

gb

ta

column

pt

45

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

60

75

90

ts

tt

105 120 135 150


ll

lp

lu beam

gt'


30

gs

gt

A.3 – 61


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.52749449E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1886E+03 0.2363E+03 0.2464E+03 0.3707E+03 3 0.98 177.24 139.96 190.35 265.51 0.1721E+03 0.7608E+02 0.1499E+03 0.1951E+03 5 2.30 354.48 207.29 334.61 450.75 0.8138E+02 0.3609E+02 0.7693E+02 0.1006E+03 7 6.04 464.90 292.07 471.74 657.40 0.2177E+02 0.1540E+02 0.1651E+02 0.3017E+02 9 12.07 542.36 359.52 541.99 761.73 0.9535E+01 0.8444E+01 0.1005E+02 0.9887E+01 11 18.11 604.89 402.07 597.98 803.39 0.9044E+01 0.5970E+01 0.8608E+01 0.4805E+01 13 24.14 654.15 433.81 649.63 825.60 0.6839E+01 0.4677E+01 0.8843E+01 0.2821E+01 15 30.18 711.41 459.46 727.70 839.39 0.1736E+02 0.3872E+01 0.1411E+02 0.1848E+01 17 36.21 830.76 481.06 814.90 848.74 0.1777E+02 0.3322E+01 0.1462E+02 0.1302E+01 19 42.25 918.67 499.84 901.72 855.51 0.1141E+02 0.2918E+01 0.1395E+02 0.9648E+00 21 48.28 972.75 516.47 981.58 860.62 0.8973E+01 0.2610E+01 0.1245E+02 0.7432E+00 23 54.32 1036.59 531.47 1051.40 864.62 0.1209E+02 0.2365E+01 0.1066E+02 0.5894E+00 25 60.35 1105.42 545.11 1110.42 867.82 0.1008E+02 0.2166E+01 0.8956E+01 0.4788E+00 27 66.39 1161.07 557.80 1160.05 870.45 0.8012E+01 0.1999E+01 0.7532E+01 0.3963E+00 29 72.42 1203.09 569.41 1202.01 872.64 0.6129E+01 0.1860E+01 0.6439E+01 0.3334E+00 31 78.46 1238.63 580.27 1238.37 874.50 0.6833E+01 0.1740E+01 0.5644E+01 0.2842E+00 33 84.49 1279.03 590.44 1270.63 876.09 0.6947E+01 0.1637E+01 0.5091E+01 0.2452E+00 35 90.53 1322.50 600.04 1300.17 877.48 0.4488E+01 0.1546E+01 0.4717E+01 0.2135E+00 37 95.97 1312.93 608.18 1325.18 878.57 -0.4327E+02 0.1473E+01 0.4492E+01 0.1900E+00 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 62



1) 2)

lu = 4.3307" gc = 2.2047" pc = 2.1654" tt = 0.4724" gt’= 2.1654" rt = 4.7244" ps = 2.1654" nt’= 2 X 1 2

= 4.3307" = 1.3780" = 1 X 3 = 7.8740" = 3.2480" = 4.7244"

ns = 2 X

ll cu nb ls gs qs

Major parameters

ns’= 2 X

1

ta = 0.2756" cl = 1.3780" nc = 1 X 3 ts = 0.4724" gs’= 2.1654" rs = 4.7244"

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 1315.09 43.99 27 1334.25 46.02 28 1353.07 48.03 29 1396.93 50.01 30 1406.36 52.01 31 1461.63 54.03 32 1466.81 56.01 33 1516.85 58.01 34 1520.75 60.03 35 1566.90 62.00 36 1591.61 64.03 37 1599.68 66.04 38 1651.35 68.04 39 1680.58 69.99 40 1691.99 72.10 41 1705.29 74.02 42 1742.67 76.00 43 1779.07 77.99 44 1792.05 80.03 45 1798.21 82.01 46 1823.59 84.00 47 1861.90 86.03 48 1880.78 88.01 49 1909.69 90.11

Fy = 315 MPa, Fu = 469 MPa for web-angle

= 7.0866" = 2.1654" = 2.1654" = 7.8740" = 3.2480" = 4.7244" = 2.1654" = 2 X 2

Japan

Fasteners: F10T- -M20 7/8" Oversize holes Material : SS400 Fy = 40.90 ksi Fu = 65.12 ksi

M. Komuro et al. (2002) W18-m

-H400x200x8x13 L150x100x12 L90x90x7

: :


Remark



Tested by Test Id.


0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

14

gb

ta

column

pt

42

pb cl ps

cu pb

gs'

pc

pc

gc

qs

qt

rs ls

lt rt

56

70

84

98

ts

tt

112 126 140

Material : SS400 Fy = 40.90 ksi : Experimental : Polynominal : M. Exponential : Power model, n = 0.80

ll

lp

lu beam

gt'


28

gs

gt

A.3 – 63


Moment ( kip-inch )

R tc A3 P3


( R : X 1/1000 radians )

Q3 =



0.21652213E+05

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5436E+03 0.7577E+03 0.6281E+03 0.7010E+03 3 0.49 244.42 293.88 256.29 241.21 0.4669E+03 0.4172E+03 0.4283E+03 0.3716E+03 5 1.52 455.30 557.16 455.30 509.23 0.9668E+02 0.1669E+03 0.4835E+02 0.1862E+03 7 5.07 586.57 885.04 594.96 862.85 0.2026E+02 0.5756E+02 0.1024E+02 0.5519E+02 9 9.00 672.03 1058.84 677.20 1011.62 0.1861E+02 0.3489E+02 0.3770E+02 0.2620E+02 11 14.00 727.92 1201.83 729.80 1106.88 0.1421E+02 0.2386E+02 0.2073E+02 0.1393E+02 13 18.01 829.29 1287.49 822.29 1153.06 0.2609E+02 0.1924E+02 0.2392E+02 0.9539E+01 15 22.09 904.68 1359.32 916.88 1186.28 0.2179E+02 0.1617E+02 0.2214E+02 0.6957E+01 17 26.02 999.88 1418.55 999.38 1210.30 0.2294E+02 0.1408E+02 0.1991E+02 0.5375E+01 19 30.02 1091.51 1471.51 1075.43 1229.47 0.1762E+02 0.1247E+02 0.1822E+02 0.4277E+01 21 34.01 1135.38 1518.70 1145.66 1244.89 0.1445E+02 0.1123E+02 0.1706E+02 0.3496E+01 23 38.00 1228.63 1561.44 1211.97 1257.63 0.1845E+02 0.1023E+02 0.1622E+02 0.2917E+01 25 42.03 1257.23 1601.33 1275.88 1268.45 0.1727E+02 0.9392E+01 0.1552E+02 0.2472E+01 27 46.02 1334.25 1637.39 1336.58 1277.60 0.9402E+01 0.8706E+01 0.1492E+02 0.2128E+01 29 50.01 1396.93 1670.89 1395.00 1285.52 0.1348E+02 0.8122E+01 0.1437E+02 0.1853E+01 31 54.03 1461.63 1702.48 1451.80 1292.51 0.1487E+02 0.7615E+01 0.1389E+02 0.1629E+01 33 58.01 1516.85 1731.87 1506.26 1298.61 0.1353E+02 0.7177E+01 0.1348E+02 0.1446E+01 35 62.00 1566.90 1759.52 1559.36 1304.07 0.1788E+02 0.6792E+01 0.1314E+02 0.1293E+01 37 66.04 1599.68 1786.59 1611.88 1309.02 0.1495E+02 0.6440E+01 0.1287E+02 0.1162E+01 39 69.99 1680.58 1811.23 1662.27 1313.39 0.1039E+02 0.6139E+01 0.1265E+02 0.1053E+01 41 74.02 1705.29 1835.68 1712.91 1317.44 0.1281E+02 0.5856E+01 0.1249E+02 0.9577E+00 43 77.99 1779.07 1858.15 1762.22 1321.07 0.1240E+02 0.5611E+01 0.1236E+02 0.8763E+00 45 82.01 1798.21 1880.46 1811.71 1324.45 0.7920E+01 0.5379E+01 0.1227E+02 0.8044E+00 47 86.03 1861.90 1901.43 1860.88 1327.55 0.1414E+02 0.5172E+01 0.1220E+02 0.7412E+00 49 90.11 1909.69 1922.33 1910.53 1330.46 0.1377E+02 0.4975E+01 0.1215E+02 0.6848E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.81341667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.10125710E+04 0.68878219E+04 -0.31898333E+05 0.59529603E+05 -0.56465008E+05 Rj0 = 0.7400 1.5200 3.0000 9.0000 RKj = -0.11850784E+03 0.10460252E+03 0.68961362E+02 -0.43027321E+02



A.3 – 64



1) 2)

lu = 2.1654" gc = 2.2047" pc = 2.1654" tt = 0.4724" gt’= 2.1654" rt = 4.7244" ps = 2.1654" nt’= 2 X 1 2

= 2.1654" = 1.3780" = 1 X 5 = 7.8740" = 3.2480" = 4.7244"

ns = 2 X

ll cu nb ls gs qs

Major parameters

ns’= 2 X

1

------------------------------

gb

ta

column


ta = 0.2756" cl = 1.3780" nc = 1 X 5 ts = 0.4724" gs’= 2.1654" rs = 4.7244"


Fy = 315 MPa, Fu = 469 MPa for web-angle

= 11.4173" = 2.1654" = 2.1654" = 7.8740" = 3.2480" = 4.7244" = 2.1654" = 2 X 2

Japan



-H400x200x8x13 L150x100x12 L90x90x7

: :


Remark



Tested by Test Id.


Moment ( kip-inch )

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

0

gs

gt

15

pt

45

ll

lp

gs'

pc

pc

gc

rs ls

qs

qt

60

75

90

ts

tt

105 120 135 150


lu beam


30

pb cl ps

cu pb

gt'

lt rt

A.3 – 65


R tc A3 P3


( R : X 1/1000 radians )

Q3 =



-0.21630372E+04

-9

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5158E+03 0.7577E+03 0.5883E+03 0.7293E+03 3 0.50 258.23 298.03 244.71 268.19 0.3959E+03 0.4116E+03 0.4017E+03 0.4151E+03 5 1.02 408.67 458.39 409.57 446.97 0.2764E+03 0.2359E+03 0.2543E+03 0.2865E+03 7 2.01 579.58 629.32 586.21 665.50 0.9568E+02 0.1304E+03 0.1212E+03 0.1714E+03 9 4.02 698.18 818.41 708.32 906.50 0.3239E+02 0.7056E+02 0.2680E+02 0.8471E+02 11 7.96 782.01 1020.65 772.18 1122.34 0.1488E+02 0.3880E+02 0.1445E+02 0.3580E+02 13 12.08 835.30 1153.10 831.75 1231.69 0.1274E+02 0.2707E+02 0.1395E+02 0.1976E+02 15 15.99 860.32 1246.64 884.10 1294.13 0.1114E+02 0.2129E+02 0.1303E+02 0.1294E+02 17 20.00 953.58 1324.09 936.14 1337.65 0.2027E+01 0.1759E+02 0.1298E+02 0.9118E+01 19 24.01 1031.88 1389.28 1047.99 1369.23 0.4656E+02 0.1507E+02 0.8820E+02 0.6806E+01 21 28.01 1163.48 1445.69 1151.65 1393.24 0.3017E+02 0.1323E+02 0.2526E+02 0.5297E+01 23 32.03 1263.56 1495.90 1249.75 1412.30 0.1904E+02 0.1181E+02 0.2347E+02 0.4246E+01 25 36.01 1342.86 1540.62 1339.25 1427.63 0.2351E+02 0.1070E+02 0.2150E+02 0.3494E+01 27 39.99 1427.98 1581.37 1421.07 1440.36 0.2156E+02 0.9801E+01 0.1965E+02 0.2930E+01 29 44.07 1486.14 1619.74 1497.87 1451.37 0.1756E+02 0.9034E+01 0.1805E+02 0.2486E+01 31 48.04 1540.70 1654.33 1566.99 1460.54 0.1433E+02 0.8405E+01 0.1683E+02 0.2147E+01 33 52.00 1614.48 1686.52 1631.72 1468.49 0.1459E+02 0.7866E+01 0.1591E+02 0.1875E+01 35 56.01 1685.31 1717.09 1694.11 1475.55 0.1370E+02 0.7393E+01 0.1524E+02 0.1651E+01 37 60.02 1756.49 1746.30 1754.25 1481.78 0.1870E+02 0.6973E+01 0.1478E+02 0.1466E+01 39 64.01 1796.45 1773.17 1812.55 1487.32 0.1233E+02 0.6612E+01 0.1446E+02 0.1311E+01 41 67.97 1876.38 1798.53 1869.38 1492.25 0.2006E+02 0.6292E+01 0.1425E+02 0.1182E+01 43 72.00 1951.12 1823.58 1926.52 1496.78 0.1664E+02 0.5994E+01 0.1411E+02 0.1069E+01 45 76.03 2003.42 1846.91 1983.19 1500.89 0.1066E+02 0.5732E+01 0.1402E+02 0.9725E+00 47 80.02 2052.83 1869.53 2039.02 1504.60 0.1184E+02 0.5491E+01 0.1396E+02 0.8895E+00 49 84.00 2114.90 1890.72 2094.52 1507.99 0.1511E+02 0.5277E+01 0.1393E+02 0.8171E+00 51 88.04 2139.22 1911.83 2150.73 1511.16 0.4853E+01 0.5073E+01 0.1390E+02 0.7525E+00 53 92.04 2185.04 1931.93 2206.32 1514.05 0.1941E+02 0.4888E+01 0.1389E+02 0.6961E+00 ----------------------------------------------------------------------------------------------------------------------------





A.3 – 66



1) 2)

tt = 0.3750" gt’= 3.5000" rt = 2.7500" pt’= 2.5000" nt’= 2 X 2

ls gs qs ps ns

= 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

IV -

------------------------------


1

0.3750" 3.5000" 2.7500"

ns’= 2 X

ts = gs’= rs =

6 X 4 X 3/8 X 6 ( SEAT ) Connection cleat riveted to 1" mounting plate.

= 6.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2


Remark

lt gt qt pt nt

Fasteners: 10.9- -7/8"D 15/16" Oversize holes Material : -Fy = 47.12 ksi Fu = 62.90 ksi

Column : -Beam : W12X31.8 Angle : 6 X 6 X 3/8 X 6 ( TOP )

Major parameters

U.S.A

: :


Tested by Test Id.

Connection type : Top-and seat-angle connections Mode : All riveted

1

0 0.0

35

70

105

140

175

210

245

280

315

350

column

0.8

pt

2.4

ps gs'

qs

qt

rs ls

lt rt

3.2

4.0

4.8

5.6

6.4

7.2


beam

gt'


1.6

gs

gt

8.0

ts

tt

A.4 – 1


Moment ( kip-inch )

R f A3 P3

= Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.875000" xl = 6.000000" = 1.240000 K = 0.012981 = 5 Q1 = -1 Q2 =

( R : X 1/1000 radians )

-1

Q3 =



0.61192138E+04

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.56531667E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.54666872E+02 0.15328450E+03 -0.26722603E+04 0.94270326E+04 -0.12834518E+05 Rj0 = 3.2600 RKj = 0.99491474E+01

Frye and Morris polynominal model : t = 0.375000" xd = 12.000000" A1 = 8.460000 A2 = 1.010000 P1 = 1 P2 = 3


A.4 – 2



1) 2)

= 8.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2

IV -

------------------------------


1

0.3750" 3.5000" 2.5000"

ns’= 3 X

ts = gs’= rs =


ls gs qs ps ns

Major parameters

tt = 0.3750" gt’= 3.5000" rt = 2.5000" pt’= 2.5000" nt’= 3 X 2


Remark

= 8.0000" = 3.5000" = 2.7500" = 2.5000" = 2 X 2



lt gt qt pt nt

U.S.A

: :


Tested by Test Id.


2

0 0.0

30

60

90

120

150

180

210

240

270

300

column

0.8

pt

2.4

ps gs'

qs

qt

rs ls

lt rt

3.2

4.0

4.8

5.6

6.4

7.2


beam

gt'


1.6

gs

gt

8.0

ts

tt

A.4 – 3


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.27721739E+04

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2346E+03 0.1114E+03 0.2390E+03 0.1048E+03 2 0.04 10.53 5.00 10.43 4.63 0.2349E+03 0.1113E+03 0.2242E+03 0.1016E+03 3 0.09 21.07 9.99 20.03 9.12 0.2060E+03 0.1109E+03 0.2039E+03 0.9888E+02 4 0.16 31.95 17.38 32.61 15.62 0.1623E+03 0.1100E+03 0.1720E+03 0.9521E+02 5 0.22 42.82 24.71 43.18 21.89 0.1467E+03 0.1087E+03 0.1445E+03 0.9186E+02 6 0.31 53.22 33.48 53.86 29.21 0.1278E+03 0.1066E+03 0.1193E+03 0.8812E+02 7 0.39 63.63 42.05 62.83 36.24 0.1119E+03 0.1040E+03 0.1025E+03 0.8468E+02 8 0.51 74.59 54.81 74.66 46.56 0.8736E+02 0.9934E+02 0.8778E+02 0.7985E+02 9 0.64 85.56 66.97 85.17 56.31 0.8140E+02 0.9431E+02 0.8024E+02 0.7551E+02 10 0.78 96.29 80.11 96.27 66.83 0.7461E+02 0.8847E+02 0.7451E+02 0.7103E+02 11 0.93 107.01 92.42 106.60 76.75 0.6767E+02 0.8283E+02 0.6899E+02 0.6699E+02 12 1.11 117.83 107.04 118.58 88.64 0.5881E+02 0.7616E+02 0.6112E+02 0.6236E+02 13 1.29 128.66 120.50 129.07 99.74 0.5309E+02 0.7023E+02 0.5279E+02 0.5825E+02 14 1.53 139.57 136.46 140.44 113.08 0.4569E+02 0.6359E+02 0.4260E+02 0.5354E+02 15 1.77 150.49 150.97 149.55 125.37 0.3747E+02 0.5801E+02 0.3400E+02 0.4942E+02 16 2.01 157.50 164.29 156.84 136.77 0.2924E+02 0.5330E+02 0.2716E+02 0.4579E+02 17 2.25 164.50 176.58 163.67 147.35 0.2923E+02 0.4931E+02 0.3271E+02 0.4257E+02 18 2.49 171.51 187.98 171.00 157.20 0.2577E+02 0.4590E+02 0.2856E+02 0.3969E+02 19 2.74 176.97 198.87 177.59 166.62 0.2222E+02 0.4289E+02 0.2521E+02 0.3706E+02 20 2.98 182.43 209.08 183.44 175.43 0.2222E+02 0.4028E+02 0.2250E+02 0.3469E+02 21 3.23 187.89 218.69 188.68 183.69 0.2222E+02 0.3799E+02 0.2029E+02 0.3255E+02 22 3.47 193.35 227.77 193.43 191.44 0.1951E+02 0.3598E+02 0.1846E+02 0.3061E+02 23 3.73 197.61 236.73 197.95 199.03 0.1668E+02 0.3413E+02 0.1689E+02 0.2879E+02 24 3.98 201.88 245.23 202.09 206.17 0.1669E+02 0.3248E+02 0.1561E+02 0.2712E+02 25 4.24 206.14 253.34 206.07 212.90 0.1696E+02 0.3100E+02 0.1600E+02 0.2561E+02 26 4.47 210.14 260.40 209.70 218.70 0.1722E+02 0.2978E+02 0.1524E+02 0.2434E+02 27 4.70 214.14 267.31 213.16 224.22 0.1497E+02 0.2865E+02 0.1461E+02 0.2317E+02 28 4.96 217.36 274.42 216.85 230.03 0.1248E+02 0.2755E+02 0.1406E+02 0.2197E+02 29 5.22 220.57 281.51 220.41 235.55 0.1248E+02 0.2650E+02 0.1363E+02 0.2087E+02 30 5.48 223.78 288.08 223.88 240.79 0.1248E+02 0.2558E+02 0.1330E+02 0.1985E+02 31 5.73 227.00 294.67 227.27 245.78 0.1248E+02 0.2470E+02 0.1305E+02 0.1891E+02 32 5.99 230.21 300.82 230.60 250.53 0.1248E+02 0.2391E+02 0.1285E+02 0.1803E+02 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.61155833E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.47672488E+02 0.69077972E+03 -0.28365484E+04 0.58675891E+04 -0.62594978E+04 Rj0 = 2.1600 4.1500 RKj = 0.10860499E+02 0.14304094E+01



A.4 – 4


: :



1) 2)

tt = 0.3750" gt’= 3.5000" rt = 5.5000" rs = 5.5000" pt’= 2.5000" nt’= 4 X 2

ls = 14.0000" gs = 3.5000" rt2= 2.5000" rs2= 2.5000" ps = 2.5000" ns = 2 X 2

IV -

------------------------------


1

0.3750" 3.5000"

ns’= 4 X

ts = gs’=


= 14.0000" = 3.5000" = 2.7500" = 2.7500" = 2.5000" = 2 X 2


Remark

lt gt qt qs pt nt

U.S.A Fasteners: 10.9- -7/8"D 15/16" Oversize holes Material : -Fy = 47.12 ksi Fu = 62.90 ksi

Major parameters


Tested by Test Id.


3

0

70

140

210

280

350

420

490

560

630

700

0

column

3

pt

9

ps gs'

qs

qt

rs ls

lt rt

12

15

18

21

24

27


beam

gt'


6

gs

gt

30

ts

tt

A.4 – 5


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.16538218E+05

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12025000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.28068559E+03 -0.69724209E+02 -0.72481404E+04 0.27265045E+05 -0.36266719E+05 Rj0 = 8.1200 RKj = 0.10846612E+02



A.4 – 6


: :

R.A.Hechtman & B.G.Johnston (1947) NO 2

U.S.A


1) 2)

ls = 6.7500" gs = 3.5000" qs = 4.2500" ps’= 2.5000" ns = 2 X 2

Major parameters

tt = 0.6250" gt’= 2.5000" rt = 4.2500" ps = 2.5000" nt’= 2 X 1

ts = gs’= rs =

IV -

------------------------------


2

0.5000" 3.5000" 4.2500"

ns’= 2 X

6 X 6 X 1/2 X 6 3/4 ( SEAT ) 2 shims 5 X 1/8 X 7 are used on ten. flange.

= 6.7500" = 3.5000" = 4.2500" = 2.5000" = 2 X 2


Remark

lt gt qt pt nt

Column : W10X49 Fasteners: 10.9- -3/4"D Beam : W12X25 13/16" Oversize holes Angle : 6 X 4 X 5/8 X 6 3/4 ( TOP ) Material : -Fy = 37.50 ksi Fu = 62.50 ksi

Tested by Test Id.


4

0

70

140

210

280

350

420

490

560

630

700

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 7


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.19079206E+05

-5






A.4 – 8


: :


1) 2)

7.5000" 3.5000" 2.2500"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

Major parameters

tt = 0.5000" gt’= 2.5000" rt = 4.5000" rs = 4.5000" ps = 2.5000" nt’= 4 X 1

IV -

2

0.8750" 3.5000"

ns’= 2 X

ts = gs’=

------------------------------


6 X 6 X 7/8 X 7 1/2 ( SEAT ) 1 shims 5 X 1/8 X 7 is used on ten. flange.

= 12.0000" = 3.5000" = 4.5000" = 4.5000" = 2.5000" = 2 X 2


Remark

lt gt qt qs pt nt

U.S.A



Column : W12X65 Beam : W18X47 Angle : 6 X 4 X 1/2 X 12 ( TOP )

Tested by Test Id.


5

0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 9


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.31693988E+05

-5






A.4 – 10


: :


1) 2)

tt = 0.6250" gt’= 2.5000" rt = 4.5000" rs = 4.5000" ps = 2.5000" nt’= 4 X 1

7.5000" 3.5000" 2.2500"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

IV -

2

0.8750" 3.5000"

ns’= 2 X

ts = gs’=

------------------------------



= 12.0000" = 3.5000" = 4.5000" = 4.5000" = 2.5000" = 2 X 2

Major parameters


Remark

lt gt qt qs pt nt

U.S.A




Tested by Test Id.


6

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 11


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.41679716E+05

-5






A.4 – 12


: :


1) 2)

7.5000" 3.5000" 2.2500"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

Major parameters

tt = 0.7500" gt’= 2.5000" rt = 4.5000" rs = 4.5000" ps = 2.5000" nt’= 4 X 1

IV -

2

0.8750" 3.5000"

ns’= 2 X

ts = gs’=

------------------------------



= 12.0000" = 3.5000" = 4.5000" = 4.5000" = 2.5000" = 2 X 2


Remark

lt gt qt qs pt nt

U.S.A




Tested by Test Id.


7

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 13


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.38462406E+05

-5






A.4 – 14


: :


1) 2)

7.5000" 3.5000" 2.5000"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

Major parameters

tt = 0.5000" gt’= 2.5000" rt = 2.5000" rs = 4.5000" ps = 2.5000" nt’= 4 X 1 2

0.8750" 3.5000"

ns’= 2 X

ts = gs’=

IV -

8

------------------------------


6 X 6 X 7/8 X 7 1/2 ( SEAT ). 1 shims 5 X 1/8 X 7 is used on ten. flange. Connection cleat riveted to column web.

= 10.0000" = 3.5000" = 4.5000" = 4.5000" = 2.5000" = 2 X 2


Remark

lt gt qt qs pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 15


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.23157730E+05

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20641500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.39319400E+03 0.95807303E+04 -0.41591381E+05 0.78478363E+05 -0.68456082E+05 Rj0 = 1.0200 5.5000 11.5700 RKj = 0.21069231E+02 -0.15682501E+01 -0.43736478E+01



A.4 – 16


: :


U.S.A


1) 2)

tt = 0.5000" gt’= 2.5000" rt = 4.2500" ps = 2.5000" nt’= 2 X 1

ls = 6.7500" gs = 3.5000" qs = 4.2500" ps’= 2.5000" ns = 2 X 2

IV -

------------------------------


2

0.5000" 3.5000" 4.2500"

ns’= 2 X

ts = gs’= rs =

6 X 6 X 1/2 X 6 3/4 ( SEAT ) 1 shims 5 X 1/8 X 6 3/4 is used on ten. flange.

= 6.7500" = 3.5000" = 4.2500" = 2.5000" = 2 X 2


Remark

lt gt qt pt nt

Major parameters


Tested by Test Id.


9

0

55

110

165

220

275

330

385

440

495

550

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 17


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.10260252E+05

-5






A.4 – 18


: :


U.S.A


1) 2)

ls = 6.7500" gs = 3.5000" qs = 4.2500" ps’= 2.5000" ns = 2 X 2

Major parameters

tt = 0.5000" gt’= 2.5000" rt = 4.2500" ps = 2.5000" nt’= 2 X 1 2

0.5000" 3.5000" 4.2500"

ns’= 2 X

ts = gs’= rs =

IV - 10

------------------------------


6 X 6 X 1/2 X 6 3/4 ( SEAT ). 1 shims 5 X 1/8 X 6 3/4 is used on ten. flange. Connection cleat riveted to column web.

= 6.7500" = 3.5000" = 4.2500" = 2.5000" = 2 X 2


Remark

lt gt qt pt nt


Tested by Test Id.


0

55

110

165

220

275

330

385

440

495

550

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 19


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.58524450E+03

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21155083E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.25323634E+03 -0.97727029E+03 0.17739097E+04 -0.80689464E+03 -0.49536732E+03 Rj0 = 4.8400 14.4900 RKj = 0.76190372E+01 -0.22245866E+01



A.4 – 20


: :


1) 2)

tt = 0.5000" gt’= 2.5000" rt = 5.0000" ps = 2.5000" nt’= 2 X 1

ls = 8.0000" gs = 3.5000" qs = 5.0000" ps’= 2.5000" ns = 2 X 2 2

0.5000" 3.5000" 5.0000"

ns’= 2 X

ts = gs’= rs =

IV - 11

------------------------------


6 X 6 X 1/2 X 8 ( SEAT ). 1 shims 5 X 1/8 X 8 is used on ten. flange. Connection cleat riveted to column web.

= 8.0000" = 3.5000" = 5.0000" = 2.5000" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

60

120

180

240

300

360

420

480

540

600

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 21


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.72146069E+04

-5



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20948333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.11835104E+03 0.31487609E+03 -0.35968147E+04 0.11940052E+05 -0.15571408E+05 Rj0 = 6.8700 13.9600 RKj = 0.21889535E+01 0.23110283E+01



A.4 – 22


: :


1) 2)

tt = 0.6250" gt’= 2.5000" rt = 4.2500" rs = 4.2500" ps = 2.5000" nt’= 4 X 1

7.2500" 3.5000" 2.2500"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

IV - 12

------------------------------


2

0.6250" 3.5000"

ns’= 2 X

ts = gs’=

6 X 6 X 5/8 X 7 1/4 ( SEAT ) 2 shims 5 X 1/8 X 6 3/4 are used on ten. flange.

= 12.0000" = 3.5000" = 4.2500" = 4.2500" = 2.5000" = 2 X 2

Major parameters


Remark

lt gt qt qs pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 23


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.38320823E+05

-5






A.4 – 24


: :


1) 2)

tt = 0.6250" gt’= 2.5000" rt = 4.2500" rs = 4.2500" ps = 2.5000" nt’= 4 X 1

7.2500" 3.5000" 2.2500"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

IV - 13

------------------------------


2

0.7500" 3.5000"

ns’= 2 X

ts = gs’=


= 12.0000" = 3.5000" = 4.2500" = 4.2500" = 2.5000" = 2 X 2

Major parameters


Remark

lt gt qt qs pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 25


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.30022960E+05

-5






A.4 – 26


: :


1) 2)

7.2500" 3.5000" 2.5000"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

Major parameters

tt = 0.6250" gt’= 2.5000" rt = 2.5000" rs = 4.2500" ps = 2.5000" nt’= 4 X 1 2

0.7500" 3.5000"

ns’= 2 X

ts = gs’=

IV - 14

------------------------------


6 X 6 X 3/4 X 7 1/4 ( SEAT ). 2 shims 5 X 1/8 X 6 3/4 are used on ten. flange. Connection cleat riveted to column web.

= 10.0000" = 3.5000" = 4.2500" = 4.2500" = 2.5000" = 2 X 2


Remark

lt gt qt qs pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

3

pt

9

ps gs'

qs

qt

rs ls

lt rt

12

15

18

21

24

27


beam

gt'


6

gs

gt

30

ts

tt

A.4 – 27


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.13982810E+05

-5






A.4 – 28


: :


1) 2)

tt = 0.6250" gt’= 2.5000" rt = 4.2500" rs = 4.2500" ps = 2.5000" nt’= 4 X 1

7.5000" 3.5000" 2.6250"

ps’= 2.5000" ns = 2 X 2

ls = gs = rt2=

IV - 15

------------------------------


2

0.8750" 3.5000"

ns’= 2 X

ts = gs’=


= 12.5000" = 3.5000" = 4.2500" = 4.2500" = 2.5000" = 2 X 2

Major parameters


Remark

lt gt qt qs pt nt

U.S.A



Column : W12X65 Beam : W18X47 Angle : 6 X 4 X 5/8 X 12 1/2 ( TOP

Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 29


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.11691611E+05

-5






A.4 – 30


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 16

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1

Fasteners: A325- -3/4"D 13/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

M.J.Marley (1982) A-1/4-1

Column : W5X16 Beam : W5X16 Angle : 4 X 4 X 1/4 X 5.0

Tested by Test Id.

Connection type : Top-and seat-angle connections Mode : All bolted

0

10

20

30

40

50

60

70

80

90

100

0

7

pt

ps

beam

21

28

35

42

gs'

gt'

49 Rotation ( x 1/1000 radians )

14


gs

gt

Material : : :

column

56

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 31


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 32


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 17

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) A-1/4-2


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

4

ps

beam

12

16

20

24

gs'

gt'


8

pt


gs

gt

Material : : :

column

32

qs

qt

36

rs ls

lt rt

40

ts

tt

A.4 – 33


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 34


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 18

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) B-1/4-1


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

3

ps

beam

9

12

15

18

gs'

gt'


6

pt


gs

gt

Material : : :

column

24

qs

qt

27

rs ls

lt rt

30

ts

tt

A.4 – 35


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1960E+05 0.1486E+02 0.1482E+03 3 0.00 3.92 0.00 0.03 0.1960E+05 0.1486E+02 0.1481E+03 5 0.05 8.06 0.74 6.42 0.4369E+02 0.1484E+02 0.1103E+03 7 0.30 12.41 4.39 12.41 0.1089E+02 0.1423E+02 -0.1896E+02 9 0.85 16.55 11.49 16.44 0.5589E+01 0.1144E+02 0.6233E+01 11 1.30 20.03 16.14 20.01 0.1524E+02 0.9340E+01 0.8624E+01 13 1.65 22.97 19.18 22.81 0.5664E+01 0.8098E+01 0.7134E+01 15 2.25 26.13 23.55 26.42 0.4989E+01 0.6578E+01 0.4916E+01 17 2.95 29.18 27.72 29.27 0.3720E+01 0.5414E+01 0.3734E+01 19 3.90 31.50 32.34 31.23 0.1693E+01 0.4401E+01 0.1382E+01 21 5.10 33.53 37.11 33.44 0.1687E+01 0.3599E+01 0.2079E+01 23 6.40 35.71 41.40 36.01 0.1771E+01 0.3036E+01 0.1796E+01 25 7.80 38.33 45.34 38.25 0.1419E+01 0.2619E+01 0.1450E+01 27 9.10 39.63 48.55 39.54 0.1002E+01 0.2336E+01 0.9883E+00 29 10.40 40.93 51.44 40.88 0.1049E+01 0.2116E+01 0.1099E+01 31 11.60 42.24 53.88 42.28 0.1093E+01 0.1953E+01 0.1232E+01 33 12.88 43.28 56.27 43.32 0.5644E+00 0.1810E+01 0.4462E+00 35 14.22 44.04 58.63 43.99 0.5644E+00 0.1683E+01 0.5346E+00 37 15.70 44.86 61.02 44.82 0.5450E+00 0.1567E+01 0.5924E+00 39 17.30 45.73 63.44 45.80 0.5450E+00 0.1460E+01 0.6254E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.14419167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.16806293E+03 -0.11650263E+04 0.40541226E+04 -0.70652947E+04 0.60202375E+04 Rj0 = 0.1000 0.3000 0.5000 1.9000 3.3000 7.8000 12.2000 RKj = -0.37979664E+02 0.40563467E+02 0.14970847E+01 0.11615218E+01 -0.32664508E+01 -0.41626388E+00 -0.90583219E+00



A.4 – 36


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 19

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) B-1/4-2


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

5

pt

ps

beam

15

20

25

30

gs'

gt'


10


gs

gt

Material : : :

column

40

qs

qt

45

rs ls

lt rt

50

ts

tt

A.4 – 37


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 38


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 20

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C1-1/4-2


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

7

pt

ps

beam

21

28

35

42

gs'

gt'


14


gs

gt

Material : : :

column

56

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 39


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.40250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.30660901E+02 -0.14305337E+03 0.15959896E+03 0.52442488E+03 -0.11296924E+04 Rj0 = 8.0000 25.4000 RKj = 0.34324344E+00 -0.10297035E+00



A.4 – 40


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 21

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C2-1/4-1


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

8

pt

ps

beam

24

32

40

48

gs'

gt'


16


gs

gt

Material : : :

column

64

qs

qt

72

rs ls

lt rt

80

ts

tt

A.4 – 41


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 42


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 22

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C2-1/4-2


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

8

pt

ps

beam

24

32

40

48

gs'

gt'


16


gs

gt

Material : : :

column

64

qs

qt

72

rs ls

lt rt

80

ts

tt

A.4 – 43


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.45167500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.75034396E+01 0.31019671E+03 -0.18165213E+04 0.44649330E+04 -0.48213600E+04 Rj0 = 15.5000 32.6000 RKj = 0.27837835E+00 -0.63863389E-02



A.4 – 44


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 23

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D1-1/4-1


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

6

pt

ps

beam

18

24

30

36

gs'

gt'


12


gs

gt

Material : : :

column

48

qs

qt

54

rs ls

lt rt

60

ts

tt

A.4 – 45


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 46


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 24

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D1-1/4-2


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

8

pt

ps

beam

24

32

40

48

gs'

gt'


16


gs

gt

Material : : :

column

64

qs

qt

72

rs ls

lt rt

80

ts

tt

A.4 – 47


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.50082500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.10803469E+02 -0.28416414E+02 -0.17344039E+03 0.82037161E+03 -0.11917200E+04 Rj0 = 13.0000 28.5000 RKj = 0.12951471E+00 0.92167996E-01



A.4 – 48


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 25

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D2-1/4-1


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

6

pt

ps

beam

18

24

30

36

gs'

gt'


12


gs

gt

Material : : :

column

48

qs

qt

54

rs ls

lt rt

60

ts

tt

A.4 – 49


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6824E+01 0.1486E+02 0.9138E+01 3 0.53 3.64 7.59 3.75 0.6825E+01 0.1314E+02 0.5772E+01 5 1.13 7.15 14.52 7.01 0.5064E+01 0.1005E+02 0.5323E+01 7 1.80 10.52 20.36 10.60 0.5207E+01 0.7656E+01 0.5434E+01 9 2.70 15.38 26.32 15.35 0.4821E+01 0.5775E+01 0.4972E+01 11 3.90 20.24 32.34 20.50 0.4497E+01 0.4401E+01 0.3551E+01 13 4.50 23.08 34.85 22.40 0.4166E+01 0.3954E+01 0.2807E+01 15 7.60 27.12 44.81 26.84 0.1208E+01 0.2670E+01 0.4913E+00 17 10.90 30.77 52.48 30.97 0.1074E+01 0.2044E+01 0.1006E+01 19 13.60 33.60 57.56 33.44 0.7764E-03 0.1739E+01 0.8489E+00 21 14.97 34.68 59.85 34.57 0.7903E+00 0.1622E+01 0.8148E+00 23 17.70 36.84 64.02 36.77 0.7930E+00 0.1436E+01 0.8067E+00 25 21.00 39.47 68.47 39.51 0.7866E+00 0.1270E+01 0.8632E+00 27 24.40 42.11 72.56 42.59 0.9818E+00 0.1141E+01 0.9459E+00 29 26.90 44.94 75.31 45.03 0.8995E+00 0.1064E+01 0.1002E+01 31 29.80 46.76 78.29 46.50 0.6373E+00 0.9899E+00 0.5332E+00 33 32.00 48.18 80.44 47.71 0.5263E+00 0.9406E+00 0.5624E+00 35 34.60 49.19 82.81 49.20 0.4071E+00 0.8903E+00 0.5872E+00 37 37.00 50.21 84.88 50.63 0.4250E+00 0.8495E+00 0.6028E+00 --------------------------------------------------------------------------------------------------




A.4 – 50


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 26

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D2-1/4-2


Tested by Test Id.


0

10

20

30

40

50

60

70

80

90

100

0

5

pt

ps

beam

15

20

25

30

gs'

gt'


10


gs

gt

Material : : :

column

40

qs

qt

45

rs ls

lt rt

50

ts

tt

A.4 – 51


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 52


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 27

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D3-1/4-1


Tested by Test Id.


0

5

10

15

20

25

30

35

40

45

50

0

5

column

beam

20

gs'

30

35

40


25

Material : : :

ps

15

pt

gt'


10

gs

gt

qs

qt

45

rs ls

lt rt

50

ts

tt

A.4 – 53


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7200E+01 0.1486E+02 0.8608E+01 3 0.40 2.88 5.80 2.96 0.7200E+01 0.1380E+02 0.6305E+01 5 0.90 5.60 12.05 5.62 0.4253E+01 0.1118E+02 0.4542E+01 7 1.50 8.15 17.93 8.08 0.4031E+01 0.8592E+01 0.3844E+01 9 2.37 11.36 24.31 11.40 0.3711E+01 0.6347E+01 0.3881E+01 11 3.27 14.78 29.37 14.88 0.3883E+01 0.5022E+01 0.3785E+01 13 4.20 18.41 33.63 18.18 0.3247E+01 0.4164E+01 0.3212E+01 15 5.27 21.10 37.70 21.13 0.2520E+01 0.3513E+01 0.2317E+01 17 6.80 23.65 42.58 23.83 0.1206E+01 0.2901E+01 0.1301E+01 19 9.00 25.92 48.31 25.97 0.8933E+00 0.2355E+01 0.8016E+00 21 11.40 28.07 53.48 27.93 0.8532E+00 0.1978E+01 0.8621E+00 23 13.53 29.81 57.44 29.84 0.8175E+00 0.1745E+01 0.9097E+00 25 15.80 31.69 61.18 31.83 0.8400E+00 0.1559E+01 0.8238E+00 27 18.15 33.61 64.66 33.56 0.7878E+00 0.1411E+01 0.6465E+00 29 20.43 34.91 67.74 34.83 0.3529E+00 0.1295E+01 0.4636E+00 31 22.70 35.71 70.60 35.70 0.2377E+00 0.1201E+01 0.3114E+00 33 24.70 35.98 72.92 36.09 0.1360E+00 0.1131E+01 0.1453E+00 35 26.87 36.25 75.30 36.31 0.1131E+00 0.1065E+01 0.6791E-01 37 29.20 36.52 77.71 36.40 0.1131E+00 0.1004E+01 0.1366E-01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.29333333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.12409746E+02 0.38440288E+03 -0.23538034E+04 0.56873694E+04 -0.60174304E+04 Rj0 = 22.7000 RKj = -0.64953542E-01



A.4 – 54


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.2500" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 28

ts = 0.2500" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D3-1/4-2


Tested by Test Id.


0

5

10

15

20

25

30

35

40

45

50

0

8

column

beam

32

gs'

48

56

64


40

Material : : :

ps

24

pt

gt'


16

gs

gt

qs

qt

72

rs ls

lt rt

80

ts

tt

A.4 – 55


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 56


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 29

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) A-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 57


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1721E+02 0.2101E+02 0.1658E+02 3 0.93 16.06 17.57 16.02 0.1721E+02 0.1556E+02 0.1778E+02 5 1.87 32.40 29.51 32.68 0.1779E+02 0.1057E+02 0.1757E+02 7 2.80 49.00 38.03 48.29 0.1581E+02 0.7954E+01 0.1569E+02 9 3.87 63.45 45.53 63.53 0.1355E+02 0.6265E+01 0.1289E+02 11 5.10 77.11 52.48 77.63 0.9183E+01 0.5090E+01 0.1011E+02 13 6.50 89.96 58.97 90.22 0.8614E+01 0.4243E+01 0.8058E+01 15 8.80 107.63 67.65 106.60 0.6804E+01 0.3386E+01 0.6413E+01 17 11.60 123.70 76.19 122.88 0.4824E+01 0.2762E+01 0.5236E+01 19 14.50 134.94 83.56 136.17 0.3718E+01 0.2347E+01 0.3904E+01 21 17.20 144.58 89.51 145.00 0.2642E-02 0.2074E+01 0.2654E+01 23 18.95 149.80 93.01 149.01 0.2983E+01 0.1934E+01 0.1952E+01 25 22.70 157.43 99.80 156.46 0.1206E+01 0.1699E+01 0.2039E+01 27 26.55 162.25 105.98 163.04 0.1304E+01 0.1519E+01 0.1451E+01 29 29.80 166.54 110.75 167.34 0.1337E+01 0.1399E+01 0.1227E+01 31 32.60 170.28 114.54 170.65 0.1283E+01 0.1313E+01 0.1145E+01 33 35.90 174.30 118.74 174.37 0.1257E+01 0.1226E+01 0.1116E+01 35 39.00 178.31 122.42 177.82 0.1207E+01 0.1157E+01 0.1118E+01 37 41.10 180.72 124.78 180.18 0.1149E+01 0.1116E+01 0.1125E+01 --------------------------------------------------------------------------------------------------




A.4 – 58


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 30

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) B-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 59


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6132E+02 0.2101E+02 0.6502E+02 3 0.20 12.26 4.17 11.08 0.6132E+02 0.2060E+02 0.4693E+02 5 0.30 18.40 6.21 15.43 0.4139E-01 0.2013E+02 0.4030E+02 7 1.20 35.20 21.48 38.12 0.2108E+02 0.1379E+02 0.1787E+02 9 1.70 46.40 27.69 46.64 0.2148E+02 0.1124E+02 0.1665E+02 11 2.50 62.40 35.55 59.90 0.1715E+02 0.8633E+01 0.1644E+02 13 3.50 76.00 43.15 75.59 0.1318E+02 0.6748E+01 0.1462E+02 15 4.70 91.20 50.38 91.00 0.1045E+02 0.5412E+01 0.1099E+02 17 6.30 103.20 58.11 105.12 0.7367E+01 0.4344E+01 0.6973E+01 19 8.30 117.60 65.92 116.19 0.5776E+01 0.3536E+01 0.4497E+01 21 11.00 128.00 74.50 126.60 0.3226E+01 0.2872E+01 0.3418E+01 23 13.93 135.47 82.21 135.69 0.2545E+01 0.2416E+01 0.2777E+01 25 17.20 142.40 89.51 143.48 0.1777E+01 0.2074E+01 0.1992E+01 27 20.60 148.40 96.11 148.95 0.1751E+01 0.1821E+01 0.1254E+01 29 23.65 153.60 101.39 153.70 0.1655E+01 0.1650E+01 0.1943E+01 31 26.75 159.20 106.29 159.18 0.1938E+01 0.1511E+01 0.1619E+01 33 29.80 164.26 110.75 163.80 0.1334E+01 0.1399E+01 0.1425E+01 35 32.60 168.00 114.54 167.62 -0.2224E+00 0.1313E+01 0.1319E+01 37 33.80 169.60 116.07 169.19 0.1143E+01 0.1281E+01 0.1288E+01 39 36.60 172.80 119.56 172.72 0.1085E+01 0.1211E+01 0.1238E+01 41 39.73 176.00 123.24 176.54 0.1021E+01 0.1143E+01 0.1207E+01 --------------------------------------------------------------------------------------------------




A.4 – 60


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 31

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) B-1/2-2


Tested by Test Id.


0

20

40

60

80

100

120

140

160

180

200

0

column

4

pt

12

ps

16

gs'

24

28

32


20

Material : : :

beam

gt'


8

gs

gt

qs

qt

36

rs ls

lt rt

40

ts

tt

A.4 – 61


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.30346801E+02 0.30296947E+03 0.27381845E+03 -0.37044020E+04 0.57402228E+04 Rj0 = 3.5000 5.7000 18.5000 RKj = -0.22977677E+01 0.58086230E+01 -0.18948032E+01



A.4 – 62


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 32

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C1-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

6

pt

18

ps

24

gs'

36

42

48


30

Material : : :

beam

gt'


12

gs

gt

qs

qt

54

rs ls

lt rt

60

ts

tt

A.4 – 63


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 64


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 33

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C1-1/2-2


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

6

pt

18

ps

24

gs'

36

42

48


30

Material : : :

beam

gt'


12

gs

gt

qs

qt

54

rs ls

lt rt

60

ts

tt

A.4 – 65


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 66


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 34

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C2-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

6

pt

18

ps

24

gs'

36

42

48


30

Material : : :

beam

gt'


12

gs

gt

qs

qt

54

rs ls

lt rt

60

ts

tt

A.4 – 67


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.34083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.85980949E+02 -0.83572476E+01 -0.48594731E+03 0.60484836E+03 -0.94690385E+02 Rj0 = 11.7000 33.9000 RKj = 0.17739571E+01 -0.92439601E+00



A.4 – 68


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 35

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) C2-1/2-2


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 69


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 70


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 36

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D1-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 71


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 72


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 37

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D1-1/2-2


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 73


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 74


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 38

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D2-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

8

pt

24

ps

32

gs'

48

56

64


40

Material : : :

beam

gt'


16

gs

gt

qs

qt

72

rs ls

lt rt

80

ts

tt

A.4 – 75


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 76


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 39

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D2-1/2-2


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

6

pt

18

ps

24

gs'

36

42

48


30

Material : : :

beam

gt'


12

gs

gt

qs

qt

54

rs ls

lt rt

60

ts

tt

A.4 – 77


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 78


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 40

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D3-1/2-1


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 79


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.40416667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.12486170E+03 -0.32548556E+03 -0.14087398E+04 0.65744958E+04 -0.86131890E+04 Rj0 = 11.3000 26.3000 RKj = 0.33721891E+00 0.64830197E+00



A.4 – 80


: :


1) 2)

= 5.0000" = -" = -" = 2 X 1

tt = 0.5000" gt’= -" rt = -" nt’= 2 X 1


Remark

lt gt qt nt

U.S.A

= 5.0000" = -" = -" = 2 X 1

------------------------------


ls gs qs ns

IV - 41

ts = 0.5000" gs’= -" rs = -" ns’= 2 X 1


Major parameters

M.J.Marley (1982) D3-1/2-2


Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

7

pt

21

ps

28

gs'

42

49

56


35

Material : : :

beam

gt'


14

gs

gt

qs

qt

63

rs ls

lt rt

70

ts

tt

A.4 – 81


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2678E+02 0.2101E+02 0.2883E+02 3 0.60 16.07 11.96 16.72 0.2795E+02 0.1808E+02 0.2651E+02 5 1.10 30.53 20.06 29.27 0.2499E+02 0.1443E+02 0.2370E+02 7 1.80 44.17 28.79 44.55 0.1917E+02 0.1083E+02 0.2007E+02 9 2.70 61.04 37.23 60.90 0.4157E-01 0.8167E+01 0.1644E+02 11 3.15 67.87 40.70 67.96 0.1517E+02 0.7296E+01 0.1499E+02 13 4.17 81.12 47.36 81.76 0.1134E+02 0.5924E+01 0.1225E+02 15 5.30 93.97 53.48 94.18 0.1095E+02 0.4945E+01 0.9756E+01 17 6.60 107.63 59.39 105.30 0.8922E+01 0.4195E+01 0.7436E+01 19 9.30 119.28 69.31 120.83 0.3284E+01 0.3250E+01 0.4480E+01 21 11.70 129.72 76.47 130.22 0.5252E+01 0.2745E+01 0.3542E+01 23 14.50 140.96 83.56 139.75 0.2944E+01 0.2347E+01 0.3336E+01 25 17.65 150.60 90.43 150.10 0.3164E+01 0.2036E+01 0.3203E+01 27 20.65 159.04 96.20 159.22 0.2382E+01 0.1818E+01 0.2834E+01 29 23.40 165.06 100.98 166.35 0.2006E+01 0.1663E+01 0.2342E+01 31 26.15 171.08 105.37 172.07 0.2382E+01 0.1536E+01 0.1819E+01 33 29.10 177.11 109.73 176.67 0.1755E+01 0.1424E+01 0.1312E+01 35 32.25 181.52 114.09 180.97 0.1037E+01 0.1323E+01 0.1446E+01 37 35.10 184.74 117.74 184.66 0.1237E+01 0.1246E+01 0.1160E+01 39 38.05 187.96 121.29 187.75 0.9745E+00 0.1178E+01 0.9501E+00 41 41.20 190.36 124.90 190.49 0.5320E+00 0.1114E+01 0.8014E+00 --------------------------------------------------------------------------------------------------




A.4 – 82


: :


1) 2)

IV - 42

1

0.3937" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

5.9055" -" -"

ns = 2 X

ls = gs = qs =

Major parameters

tt = 0.3937" gt’= -" rt = -" ps = -" nt’= 2 X 1

Grade 8.8 bolts at column Hsfg bolts in two rows at beam.

= 5.9055" = -" = -" = -" = 2 X 2


Remark

lt gt qt pt nt

U.S.A

Fasteners: G8.8- -M20 7/8" Oversize holes Material : -Fy = -ksi Fu = -ksi

S.M.Maxwell et al. (1981) A1

Column : 305 X 305 X UC 97 Beam : 457 X 191 X UB 67 Angle : 150 X 90 X 10 X 150 MM

Tested by Test Id.


0

70

140

210

280

350

420

490

560

630

700

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

qs

qt

18

rs ls

lt rt

20

ts

tt

A.4 – 83


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.99583333E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.10573124E+03 0.19981288E+04 -0.11951490E+05 0.30972569E+05 -0.35206273E+05 Rj0 = 2.5000 5.8000 RKj = 0.14561508E+02 0.93803764E+01



A.4 – 84


: :


1) 2)

tt = 0.3937" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 43

1

0.3937" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

7.8740" -" -"

ns = 2 X

ls = gs = qs =


= 7.8740" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

95

190

285

380

475

570

665

760

855

950

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

qs

qt

18

rs ls

lt rt

20

ts

tt

A.4 – 85


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 86


: :


1) 2)

tt = 0.3937" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 44

1

0.3937" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

5.9055" -" -"

ns = 2 X

ls = gs = qs =


= 5.9055" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

85

170

255

340

425

510

595

680

765

850

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

qs

qt

18

rs ls

lt rt

20

ts

tt

A.4 – 87


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1682E+03 0.1508E+03 0.1101E+03 2 0.17 29.44 26.25 27.41 0.1682E+03 0.1485E+03 0.1829E+03 3 0.35 58.88 51.75 59.89 0.1682E+03 0.1424E+03 0.1824E+03 4 0.53 88.32 75.94 90.27 0.1682E+03 0.1338E+03 0.1640E+03 5 0.70 117.76 98.52 117.36 0.1553E+03 0.1242E+03 0.1463E+03 6 0.95 151.94 127.88 151.64 0.1368E+03 0.1108E+03 0.1296E+03 7 1.20 186.13 154.07 182.82 0.1211E+03 0.9900E+02 0.1207E+03 8 1.47 213.99 179.01 214.18 0.1045E+03 0.8838E+02 0.1149E+03 9 1.73 241.84 201.37 244.16 0.1045E+03 0.7963E+02 0.1101E+03 10 2.00 269.70 221.61 272.89 0.1089E+03 0.7241E+02 0.1053E+03 11 2.30 303.89 242.30 303.69 0.1140E+03 0.6573E+02 0.1001E+03 12 2.60 338.08 261.17 332.99 0.9971E+02 0.6023E+02 0.9535E+02 13 3.00 370.36 284.03 370.04 0.8072E+02 0.5427E+02 0.9007E+02 14 3.40 402.65 304.74 405.18 0.8309E+02 0.4948E+02 0.8579E+02 15 3.80 436.84 323.72 438.73 0.8547E+02 0.4554E+02 0.8196E+02 16 4.20 471.02 341.26 470.73 0.8100E+02 0.4225E+02 0.7800E+02 17 4.65 505.21 359.56 504.73 0.7597E+02 0.3915E+02 0.7297E+02 18 5.10 539.40 376.57 536.29 0.6506E+02 0.3652E+02 0.6718E+02 19 5.43 558.39 388.45 557.90 0.5697E+02 0.3483E+02 0.6246E+02 20 5.77 577.38 399.80 577.90 0.5697E+02 0.3331E+02 0.5750E+02 21 6.10 596.38 410.67 596.22 0.5249E+02 0.3193E+02 0.5242E+02 22 6.55 617.27 424.66 618.26 0.4643E+02 0.3028E+02 0.4559E+02 23 7.00 638.16 437.95 637.29 0.3799E+02 0.2881E+02 0.3904E+02 24 7.45 651.46 450.61 653.47 0.2955E+02 0.2750E+02 0.3296E+02 25 7.90 664.75 462.72 667.05 0.2785E+02 0.2633E+02 0.2748E+02 26 8.23 673.62 471.49 675.59 0.2659E+02 0.2552E+02 0.2385E+02 27 8.57 682.48 479.75 682.99 0.2659E+02 0.2479E+02 0.2057E+02 28 8.90 691.34 488.01 689.35 0.2098E+02 0.2409E+02 0.1766E+02 29 9.30 697.04 497.37 695.78 0.1425E+02 0.2332E+02 0.1460E+02 30 9.70 702.74 506.70 701.09 0.1425E+02 0.2260E+02 0.1201E+02 --------------------------------------------------------------------------------------------------




A.4 – 88


: :


1) 2)

tt = 0.3937" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 45

1

0.3937" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

7.8740" -" -"

ns = 2 X

ls = gs = qs =


= 7.8740" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 89


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2143E+03 0.1844E+03 0.1020E+03 2 0.20 42.87 36.64 40.32 0.2143E+03 0.1808E+03 0.2482E+03 3 0.40 85.74 71.93 88.34 0.2143E+03 0.1713E+03 0.2212E+03 4 0.60 128.60 104.96 127.68 0.1858E+03 0.1587E+03 0.1739E+03 5 0.90 171.47 149.56 173.32 0.1429E+03 0.1387E+03 0.1381E+03 6 1.20 214.33 188.45 213.92 0.1429E+03 0.1211E+03 0.1358E+03 7 1.50 257.20 222.53 255.62 0.1423E+03 0.1066E+03 0.1420E+03 8 1.77 295.02 249.53 293.88 0.1418E+03 0.9619E+02 0.1440E+03 9 2.03 332.84 273.99 331.91 0.1418E+03 0.8757E+02 0.1405E+03 10 2.30 370.67 296.36 368.45 0.1276E+03 0.8039E+02 0.1330E+03 11 2.57 400.93 316.97 402.71 0.1135E+03 0.7435E+02 0.1237E+03 12 2.83 431.19 336.09 434.44 0.1135E+03 0.6921E+02 0.1145E+03 13 3.10 461.45 353.94 463.85 0.1078E+03 0.6480E+02 0.1063E+03 14 3.50 501.16 378.71 504.43 0.9929E+02 0.5922E+02 0.9722E+02 15 3.90 540.88 401.45 542.09 0.9805E+02 0.5463E+02 0.9157E+02 16 4.35 584.38 425.04 582.39 0.9667E+02 0.5034E+02 0.8785E+02 17 4.80 627.88 446.86 621.30 0.8677E+02 0.4675E+02 0.8512E+02 18 5.13 654.35 462.05 649.31 0.7942E+02 0.4445E+02 0.8293E+02 19 5.47 680.83 476.53 676.53 0.7942E+02 0.4240E+02 0.8024E+02 20 5.80 707.30 490.35 702.74 0.6998E+02 0.4056E+02 0.7692E+02 21 6.13 727.48 503.59 727.74 0.6051E+02 0.3890E+02 0.7297E+02 22 6.47 747.65 516.30 751.33 0.6051E+02 0.3739E+02 0.6849E+02 23 6.80 767.82 528.76 773.36 0.5863E+02 0.3598E+02 0.6362E+02 24 7.13 786.73 540.31 793.71 0.5673E+02 0.3474E+02 0.5850E+02 25 7.47 805.64 551.90 812.35 0.5673E+02 0.3356E+02 0.5329E+02 26 7.80 824.56 562.71 829.25 0.5296E+02 0.3250E+02 0.4813E+02 27 8.13 840.95 573.54 844.45 0.4917E+02 0.3149E+02 0.4311E+02 28 8.47 857.34 583.72 858.02 0.4917E+02 0.3058E+02 0.3833E+02 29 8.80 873.73 593.92 870.04 0.4256E+02 0.2971E+02 0.3386E+02 30 9.25 888.86 606.90 884.01 0.3361E+02 0.2864E+02 0.2835E+02 31 9.70 903.98 619.79 895.66 0.3361E+02 0.2764E+02 0.2350E+02 --------------------------------------------------------------------------------------------------




A.4 – 90


: :


1) 2)

tt = 0.4724" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 46

1

0.4724" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

5.9055" -" -"

ns = 2 X

ls = gs = qs =


= 5.9055" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A


S.M.Maxwell et al. (1981) B1


Tested by Test Id.


0

100

200

300

400

500

600

700

800

900

1000

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 91


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1825E+03 0.1651E+03 0.5048E+01 2 0.20 36.49 32.81 30.20 0.1825E+03 0.1619E+03 0.2268E+03 3 0.40 72.98 64.42 75.78 0.1825E+03 0.1535E+03 0.2131E+03 4 0.60 109.48 94.01 113.25 0.1639E+03 0.1421E+03 0.1624E+03 5 0.87 146.58 129.77 150.35 0.1392E+03 0.1262E+03 0.1225E+03 6 1.13 183.69 161.43 181.59 0.1392E+03 0.1117E+03 0.1157E+03 7 1.40 220.80 189.55 213.13 0.1261E+03 0.9951E+02 0.1215E+03 8 1.70 254.20 217.66 250.46 0.1113E+03 0.8832E+02 0.1263E+03 9 2.00 287.60 242.76 288.13 0.1113E+03 0.7932E+02 0.1236E+03 10 2.30 321.00 265.42 323.95 0.1043E+03 0.7200E+02 0.1145E+03 11 2.63 353.16 288.27 359.94 0.9649E+02 0.6537E+02 0.1013E+03 12 2.97 385.33 309.13 391.57 0.9649E+02 0.5994E+02 0.8880E+02 13 3.30 417.49 328.33 419.47 0.9053E+02 0.5541E+02 0.7920E+02 14 3.75 454.60 352.10 453.18 0.8247E+02 0.5038E+02 0.7161E+02 15 4.20 491.71 373.82 484.65 0.7628E+02 0.4629E+02 0.6884E+02 16 4.65 523.25 393.86 515.51 0.7009E+02 0.4288E+02 0.6854E+02 17 5.10 554.80 412.49 546.39 0.6391E+02 0.4001E+02 0.6868E+02 18 5.55 580.77 429.93 577.19 0.5772E+02 0.3755E+02 0.6797E+02 19 6.00 606.74 446.33 607.35 0.5567E+02 0.3542E+02 0.6587E+02 20 6.45 630.87 461.84 636.25 0.5361E+02 0.3355E+02 0.6234E+02 21 6.90 655.00 476.56 663.28 0.5224E+02 0.3190E+02 0.5764E+02 22 7.30 675.40 489.05 685.39 0.5102E+02 0.3058E+02 0.5281E+02 23 7.70 695.81 501.04 705.48 0.5491E+02 0.2939E+02 0.4764E+02 24 8.05 716.22 511.33 721.35 0.5832E+02 0.2842E+02 0.4304E+02 25 8.40 736.63 520.95 735.62 0.4626E+02 0.2755E+02 0.3851E+02 26 8.80 749.62 531.97 750.03 0.3248E+02 0.2660E+02 0.3356E+02 27 9.20 762.61 542.26 762.52 0.4219E+02 0.2575E+02 0.2895E+02 28 9.50 777.46 549.98 770.72 0.4948E+02 0.2514E+02 0.2576E+02 29 9.80 792.30 557.53 778.00 0.4948E+02 0.2457E+02 0.2282E+02 --------------------------------------------------------------------------------------------------




A.4 – 92


: :


1) 2)

tt = 0.4724" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 47

1

0.4724" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

7.8740" -" -"

ns = 2 X

ls = gs = qs =


= 7.8740" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 93


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1373E+03 0.2020E+03 0.4983E+01 2 0.25 34.33 49.99 28.14 0.1373E+03 0.1960E+03 0.1707E+03 3 0.50 68.65 97.24 72.74 0.1538E+03 0.1810E+03 0.1758E+03 4 0.70 102.05 131.99 106.36 0.1670E+03 0.1664E+03 0.1603E+03 5 0.90 135.45 163.81 137.11 0.1670E+03 0.1520E+03 0.1483E+03 6 1.10 168.85 192.85 166.07 0.1571E+03 0.1387E+03 0.1422E+03 7 1.40 211.53 231.84 208.18 0.1423E+03 0.1217E+03 0.1392E+03 8 1.70 254.21 266.22 249.69 0.1329E+03 0.1080E+03 0.1373E+03 9 2.05 296.88 301.73 296.89 0.1219E+03 0.9539E+02 0.1318E+03 10 2.40 339.55 333.31 341.53 0.1201E+03 0.8545E+02 0.1229E+03 11 2.65 369.24 353.91 371.36 0.1188E+03 0.7959E+02 0.1157E+03 12 2.90 398.93 373.16 399.39 0.1068E+03 0.7454E+02 0.1086E+03 13 3.25 430.48 398.17 435.83 0.9014E+02 0.6854E+02 0.9991E+02 14 3.60 462.02 421.26 469.56 0.1015E+03 0.6353E+02 0.9319E+02 15 3.90 495.42 439.75 496.85 0.1113E+03 0.5984E+02 0.8899E+02 16 4.20 528.82 457.21 523.07 0.9909E+02 0.5661E+02 0.8595E+02 17 4.55 558.50 476.43 552.68 0.8482E+02 0.5331E+02 0.8340E+02 18 4.90 588.19 494.57 581.51 0.8204E+02 0.5043E+02 0.8138E+02 19 5.30 619.73 514.16 613.62 0.7885E+02 0.4754E+02 0.7914E+02 20 5.70 651.28 532.66 644.77 0.6726E+02 0.4501E+02 0.7653E+02 21 6.10 673.54 550.21 674.77 0.5567E+02 0.4278E+02 0.7332E+02 22 6.50 695.81 566.91 703.34 0.6262E+02 0.4080E+02 0.6945E+02 23 6.90 723.64 582.87 730.24 0.6959E+02 0.3901E+02 0.6499E+02 24 7.30 751.48 598.15 755.27 0.6358E+02 0.3741E+02 0.6010E+02 25 7.65 771.89 611.24 775.52 0.5832E+02 0.3610E+02 0.5559E+02 26 8.00 792.30 623.45 794.18 0.5126E+02 0.3494E+02 0.5099E+02 27 8.33 807.14 635.09 810.44 0.4453E+02 0.3388E+02 0.4663E+02 28 8.67 821.99 646.05 825.28 0.4453E+02 0.3292E+02 0.4236E+02 29 9.00 836.83 657.03 838.70 0.4454E+02 0.3200E+02 0.3824E+02 30 9.33 851.68 667.40 850.79 0.4453E+02 0.3117E+02 0.3433E+02 31 9.67 866.52 677.79 861.62 0.4453E+02 0.3036E+02 0.3066E+02 32 10.00 881.36 687.91 871.26 0.4454E+02 0.2960E+02 0.2725E+02 --------------------------------------------------------------------------------------------------




A.4 – 94


: :


1) 2)

tt = 0.4724" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 48

1

0.4724" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

5.9055" -" -"

ns = 2 X

ls = gs = qs =


= 5.9055" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 95


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 96


: :


1) 2)

tt = 0.4724" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 49

1

0.4724" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

7.8740" -" -"

ns = 2 X

ls = gs = qs =


= 7.8740" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 97


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 98


: :


1) 2)

tt = 0.5906" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 50

1

0.5906" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

5.9055" -" -"

ns = 2 X

ls = gs = qs =


= 5.9055" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A


S.M.Maxwell et al. (1981) C1


Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 99


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 100


: :


1) 2)

IV - 51

1

0.5906" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

7.8740" -" -"

ns = 2 X

ls = gs = qs =

Major parameters

tt = 0.5906" gt’= -" rt = -" ps = -" nt’= 2 X 1


= 7.8740" = -" = -" = -" = 2 X 2


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 101


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1324E+03 0.2258E+03 0.8531E+02 2 0.20 26.47 44.87 25.76 0.1425E+03 0.2215E+03 0.1539E+03 3 0.47 68.08 101.94 68.35 0.1560E+03 0.2049E+03 0.1598E+03 4 0.73 109.69 153.74 110.39 0.1560E+03 0.1833E+03 0.1564E+03 5 1.00 151.30 199.78 152.34 0.1627E+03 0.1623E+03 0.1589E+03 6 1.30 202.36 245.32 200.79 0.1702E+03 0.1420E+03 0.1639E+03 7 1.60 253.42 285.35 250.42 0.1608E+03 0.1255E+03 0.1664E+03 8 1.90 298.81 320.95 300.24 0.1513E+03 0.1123E+03 0.1652E+03 9 2.20 344.20 352.98 349.27 0.1678E+03 0.1016E+03 0.1614E+03 10 2.45 389.59 377.42 389.13 0.1816E+03 0.9415E+02 0.1574E+03 11 2.70 434.98 400.14 427.97 0.1608E+03 0.8780E+02 0.1533E+03 12 3.10 486.04 433.51 488.04 0.1277E+03 0.7936E+02 0.1472E+03 13 3.50 537.10 463.84 545.83 0.1484E+03 0.7254E+02 0.1418E+03 14 3.80 586.27 484.94 587.81 0.1639E+03 0.6822E+02 0.1380E+03 15 4.10 635.44 504.83 628.63 0.1456E+03 0.6445E+02 0.1341E+03 16 4.45 678.94 526.70 674.68 0.1243E+03 0.6061E+02 0.1290E+03 17 4.80 722.44 547.32 718.81 0.1253E+03 0.5726E+02 0.1231E+03 18 5.10 760.26 564.11 759.77 0.1261E+03 0.5471E+02 0.1336E+03 19 5.40 798.08 580.17 798.95 0.1203E+03 0.5242E+02 0.1274E+03 20 5.75 837.80 598.09 842.20 0.1135E+03 0.5000E+02 0.1196E+03 21 6.10 877.51 615.20 882.65 0.1135E+03 0.4784E+02 0.1114E+03 22 6.45 917.23 631.59 920.19 0.1135E+03 0.4588E+02 0.1030E+03 23 6.80 956.94 647.34 954.78 0.1024E+03 0.4410E+02 0.9467E+02 24 7.25 996.65 666.71 995.01 0.8825E+02 0.4204E+02 0.8422E+02 25 7.70 1036.37 685.21 1030.68 0.3638E+02 0.4020E+02 0.7441E+02 26 7.95 1038.26 695.25 1035.91 0.7560E+01 0.3924E+02 0.1840E+02 27 8.20 1040.15 705.06 1039.90 0.4124E+01 0.3834E+02 0.1358E+02 28 8.50 1040.15 716.19 1043.15 0.0000E+00 0.3735E+02 0.8201E+01 29 8.80 1040.15 727.39 1044.86 0.3150E+01 0.3639E+02 0.3258E+01 30 9.10 1042.04 738.31 1045.15 0.6300E+01 0.3548E+02 -0.1249E+01 31 9.40 1043.93 748.56 1044.16 0.2864E+01 0.3467E+02 -0.5329E+01 32 9.65 1043.93 757.23 1042.43 0.0000E+00 0.3399E+02 -0.8416E+01 33 9.90 1043.93 765.72 1039.97 0.0000E+00 0.3335E+02 -0.1123E+02 --------------------------------------------------------------------------------------------------




A.4 – 102


: :


1) 2)

tt = 0.5906" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 52

1

0.5906" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

5.9055" -" -"

ns = 2 X

ls = gs = qs =


= 5.9055" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 103


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 104


: :


1) 2)

tt = 0.5906" gt’= -" rt = -" ps = -" nt’= 2 X 1

IV - 53

1

0.5906" -" -"

ns’= 2 X

ts = gs’= rs =

------------------------------


2

7.8740" -" -"

ns = 2 X

ls = gs = qs =


= 7.8740" = -" = -" = -" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

2

pt

6

ps

8

gs'

12

14

16


10

Material : : :

beam

gt'


4

gs

gt

18

qs

qt

rs ls

lt rt

20

ts

tt

A.4 – 105


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2184E+03 0.2258E+03 0.1665E+03 3 0.35 76.43 77.52 77.45 0.2184E+03 0.2133E+03 0.2241E+03 5 0.70 152.86 147.58 151.79 0.2109E+03 0.1861E+03 0.2065E+03 7 1.03 220.79 205.13 221.07 0.2038E+03 0.1598E+03 0.2097E+03 9 1.37 289.99 254.65 290.73 0.2114E+03 0.1380E+03 0.2061E+03 11 1.70 360.44 297.66 357.20 0.1925E+03 0.1208E+03 0.1915E+03 13 2.10 428.38 342.65 429.33 0.1698E+03 0.1049E+03 0.1693E+03 15 2.53 496.32 385.16 498.32 0.1456E+03 0.9193E+02 0.1506E+03 17 3.00 564.26 425.48 565.80 0.1456E+03 0.8130E+02 0.1401E+03 19 3.47 632.20 461.42 630.15 0.1456E+03 0.7306E+02 0.1362E+03 21 4.05 713.35 501.59 711.14 0.1348E+03 0.6505E+02 0.1398E+03 23 4.75 803.93 544.44 806.30 0.1240E+03 0.5772E+02 0.1308E+03 25 5.45 888.85 582.78 892.69 0.1186E+03 0.5205E+02 0.1150E+03 27 6.20 973.78 619.96 971.20 0.1085E+03 0.4726E+02 0.9398E+02 29 6.85 1013.41 649.69 1011.80 -0.1510E+02 0.4384E+02 0.1783E+02 31 7.40 1011.52 672.97 1017.64 0.6280E+01 0.4140E+02 0.3695E+01 33 8.05 1015.29 699.04 1015.28 0.5400E+01 0.3889E+02 -0.1049E+02 --------------------------------------------------------------------------------------------------




A.4 – 106


: :


1) 2)

RSA 125x75x8 SEAT

1

0.3150" 1.3780" 2.9921"

nt’= 2 X

tt = gt’= rt =


Remark

lt = 4.7638" gt = 2.1654" qt = 2.2441" ps’= 1.9685" nt = 2 X 1 2

0.3150" 1.7720" 2.9921"

ns’= 2 X

ts = gs’= rs =

------------------------------


1

4.7638" 1.9685" 2.2441"

ns = 2 X

ls = gs = qs =

Major parameters

IV - 54

United Kingdom


J.B.Davison et al. (1987) JT/08

Column : UC 152x152x23 Beam : UB 254x102x22 Angle : RSA 80x60x8 TOP

Tested by Test Id.


0

25

50

75

100

125

150

175

200

225

250

0

column

8

pt

24

ps

32

gs'

48

56

64


40

Material : : :

beam

gt'


16

gs

gt

qs

qt

72

rs ls

lt rt

80

ts

tt

A.4 – 107


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-5





A.4 – 108


: :


1) 2)

= 8.0000" = 3.0000" = 3.5000" = 2.5000" = 2 X 2

tt = 0.3750" gt’= 2.5000" rt = 5.5000" ps = 2.5000" nt’= 2 X 1


Remark

lt gt qt pt nt

U.S.A.

2

IV - 55

1

0.3750" 2.5000" 5.5000"

ns’= 2 X

ts = gs’= rs =

------------------------------


ns = 2 X

ls = gs = qs =

8.0000" 3.0000" 3.5000"


Major parameters

A.Azizinamini (1985) ---

Column : W12x96 Beam : W14x38 Angle : L6x4x3/8

Tested by Test Id.


0

75

150

225

300

375

450

525

600

675

750

0

column

4

pt

12

ps gs'

qs

qt

rs ls

lt rt

16

20

24

28

32

36


beam

gt'


8

gs

gt

40

ts

tt

A.4 – 109


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.17996149E+04

-5






A.4 – 110


: :


1) 2)

= 8.0000" = 3.0000" = 3.5000" = 2.5000" = 2 X 2

tt = 0.5000" gt’= 2.5000" rt = 5.5000" ps = 2.5000" nt’= 2 X 1


Remark

lt gt qt pt nt

U.S.A.

2

IV - 56

1

0.5000" 2.5000" 5.5000"

ns’= 2 X

ts = gs’= rs =

------------------------------


ns = 2 X

ls = gs = qs =

8.0000" 3.0000" 3.5000"


Major parameters

A.Azizinamini (1985) ---


Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

pt

ps

beam

gs'

gt'

4

12

16

20

24


8


gs

gt

32

36

qs

qt

rs ls

lt rt

40

ts

tt

A.4 – 111


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.10594418E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5619E+04 0.1638E+03 0.1916E+04 0.3974E+03 2 0.02 118.00 3.44 38.23 8.23 0.4523E+04 0.1638E+03 0.1727E+04 0.3867E+03 3 0.10 142.00 16.68 152.00 38.18 0.3260E+05 0.1630E+03 0.1111E+04 0.3542E+03 4 0.10 175.00 16.68 152.00 38.18 0.3265E+05 0.1630E+03 0.1111E+04 0.3542E+03 5 0.20 206.00 31.74 229.70 69.66 0.5740E+03 0.1608E+03 0.5897E+03 0.3236E+03 6 0.25 248.00 41.01 256.54 87.94 0.5877E+03 0.1588E+03 0.3451E+03 0.3070E+03 7 0.41 283.00 64.66 273.34 131.69 0.3367E+03 0.1520E+03 -0.7867E+02 0.2700E+03 8 0.47 310.00 75.17 310.00 150.07 0.3258E+03 0.1482E+03 0.5200E+03 0.2554E+03 9 0.66 341.00 101.87 341.00 194.62 0.1601E+03 0.1372E+03 0.1631E+03 0.2223E+03 10 0.97 387.00 140.99 387.00 255.87 0.1290E+03 0.1195E+03 0.1711E+03 0.1815E+03 11 1.53 437.00 200.62 437.00 342.87 0.7805E+02 0.9355E+02 0.1901E+03 0.1318E+03 12 2.06 473.00 245.50 472.74 404.32 0.5813E+02 0.7709E+02 0.1207E+03 0.1021E+03 13 3.25 516.00 322.90 515.86 500.35 0.3211E+02 0.5559E+02 0.4207E+02 0.6392E+02 14 4.68 555.00 391.93 556.54 573.69 0.2198E+02 0.4233E+02 0.1762E+02 0.4121E+02 15 6.31 581.00 453.49 580.21 628.67 0.1616E+02 0.3381E+02 0.1424E+02 0.2764E+02 16 7.96 608.00 504.50 605.84 667.26 0.1522E+02 0.2844E+02 0.1652E+02 0.1981E+02 17 9.44 629.00 543.94 630.41 693.06 0.1553E+02 0.2506E+02 0.1637E+02 0.1535E+02 18 11.30 661.00 587.51 659.53 717.89 0.1387E+02 0.2195E+02 0.1492E+02 0.1161E+02 19 12.60 676.00 614.91 678.36 731.73 0.1334E+02 0.2027E+02 0.1412E+02 0.9767E+01 20 13.80 694.00 638.43 695.04 742.62 0.1415E+02 0.1897E+02 0.1373E+02 0.8433E+01 21 15.50 716.00 669.33 718.21 755.66 0.1372E+02 0.1743E+02 0.1361E+02 0.6972E+01 22 17.80 750.00 707.45 749.72 769.94 0.1536E+02 0.1577E+02 0.1382E+02 0.5536E+01 23 20.00 785.00 740.70 780.43 780.98 0.1438E+02 0.1451E+02 0.1409E+02 0.4546E+01 24 21.50 805.00 761.90 801.68 787.39 0.1260E+02 0.1377E+02 0.1424E+02 0.4017E+01 25 23.20 825.00 784.68 825.98 793.79 0.1235E+02 0.1304E+02 0.1435E+02 0.3524E+01 26 24.90 847.00 806.29 850.45 799.42 0.1294E+02 0.1240E+02 0.1443E+02 0.3117E+01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21275000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.35769220E+04 -0.16129222E+05 0.37458815E+05 -0.50995838E+05 0.36657703E+05 Rj0 = 0.4100 0.4800 0.6600 0.9700 1.5300 2.0600 RKj = 0.71486884E+03 -0.26968864E+03 0.66416616E+02 -0.18389540E+03 -0.19232220E+03 -0.12083787E+03



A.4 – 112


: :


1) 2)

= 6.0000" = 3.0000" = 2.7500" = 2.5000" = 2 X 2

tt = 0.3750" gt’= 2.0000" rt = 3.5000" ps = 2.5000" nt’= 2 X 1


Remark

lt gt qt pt nt

U.S.A.

2

IV - 57

1

0.3750" 2.0000" 3.5000"

ns’= 2 X

ts = gs’= rs =

------------------------------


ns = 2 X

ls = gs = qs =

6.0000" 3.0000" 2.7500"


Major parameters

W.L.Harper,Jr. (1990) TEST3

Column : W8x24 Beam : W8x21 Angle : L6x3.5x3/8

Tested by Test Id.


0

50

100

150

200

250

300

350

400

450

500

0

column

9

pt

27

ps gs'

qs

qt

rs ls

lt rt

36

45

54

63

72

81


beam

gt'


18

gs

gt

90

ts

tt

A.4 – 113


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.27095389E+05

-5






A.4 – 114


: :


Remark

lt gt qt pt nt

1) 2)

tt = 0.3750" gt’= 2.0000" rt = 3.5000" ps = 2.3750" nt’= 2 X 1 2

6.5000" 3.6250" 2.5000"

ns = 2 X

ls = gs = qs =

Major parameters

1

0.3750" 2.0000" 3.5000"

ns’= 2 X

ts = gs’= rs =

IV - 58

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 18.50 0.19 3 29.40 0.37 4 51.31 0.76 5 74.27 1.23 6 97.76 1.78 7 121.25 2.32 8 142.06 2.90 9 160.20 3.44 10 176.19 4.03 11 191.11 4.63 12 206.02 5.27 13 221.97 6.09 14 235.26 6.87 15 248.53 7.76 16 260.18 8.79 17 270.21 9.92 18 278.64 11.02 19 285.99 12.14 20 291.23 13.01 21 295.94 13.88 22 301.73 14.68 23 305.89 15.60 24 310.57 16.75 ------------------------------

1 in. thick column flange plate to minimize the column flange distortion loading rate 0.4%/s

= 6.5000" = 3.6250" = 2.5000" = 2.3750" = 2 X 2

U.S.A.


J.B. Mander et al. (1994) R1_01


Tested by Test Id.


0

40

80

120

160

200

240

280

320

360

400

0

column

3

pt

9

ps gs'

qs

qt

rs ls

lt rt

12

15

18

21

24

27


beam

gt'


6

gs

gt

30

ts

tt

A.4 – 115


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.13431746E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.9531E+02 0.4659E+02 0.9004E+02 0.1031E+03 2 0.19 18.50 8.99 16.63 18.62 0.7779E+02 0.4574E+02 0.8025E+02 0.8983E+02 3 0.37 29.40 16.88 29.78 33.64 0.6000E+02 0.4372E+02 0.6902E+02 0.8096E+02 4 0.76 51.31 32.83 52.82 62.33 0.5268E+02 0.3732E+02 0.5050E+02 0.6616E+02 5 1.23 74.27 48.61 74.23 90.30 0.4619E+02 0.3016E+02 0.4268E+02 0.5376E+02 6 1.78 97.76 63.35 97.16 116.72 0.4301E+02 0.2419E+02 0.4176E+02 0.4356E+02 7 2.32 121.25 75.39 119.75 138.40 0.3981E+02 0.2016E+02 0.4058E+02 0.3617E+02 8 2.90 142.06 86.00 141.95 157.30 0.3487E+02 0.1721E+02 0.3685E+02 0.3038E+02 9 3.44 160.20 94.77 160.69 172.62 0.3028E+02 0.1516E+02 0.3198E+02 0.2612E+02 10 4.03 176.19 103.25 178.09 187.00 0.2603E+02 0.1346E+02 0.2676E+02 0.2245E+02 11 4.63 191.11 110.83 192.66 199.42 0.2418E+02 0.1214E+02 0.2252E+02 0.1954E+02 12 5.27 206.02 118.28 206.05 211.16 0.2149E+02 0.1101E+02 0.1927E+02 0.1699E+02 13 6.09 221.97 126.86 220.76 224.05 0.1827E+02 0.9876E+01 0.1669E+02 0.1442E+02 14 6.87 235.26 134.14 233.01 234.42 0.1609E+02 0.9033E+01 0.1517E+02 0.1253E+02 15 7.76 248.53 141.89 245.99 244.85 0.1317E+02 0.8241E+01 0.1374E+02 0.1076E+02 16 8.79 260.18 149.95 259.24 255.05 0.1019E+02 0.7516E+01 0.1207E+02 0.9184E+01 17 9.92 270.21 158.05 271.71 264.60 0.8270E+01 0.6874E+01 0.1004E+02 0.7826E+01 18 11.02 278.64 165.32 281.65 272.62 0.7099E+01 0.6362E+01 0.8032E+01 0.6778E+01 19 12.14 285.99 172.23 289.61 279.75 0.6247E+01 0.5924E+01 0.6134E+01 0.5914E+01 20 13.01 291.23 177.25 294.37 284.64 0.5722E+01 0.5632E+01 0.4860E+01 0.5358E+01 21 13.88 295.94 182.03 298.11 289.09 0.6398E+01 0.5372E+01 0.3782E+01 0.4878E+01 22 14.68 301.73 186.21 300.78 292.80 0.6014E+01 0.5159E+01 0.2966E+01 0.4496E+01 23 15.60 305.89 190.85 303.15 296.76 0.4320E+01 0.4937E+01 0.2207E+01 0.4107E+01 24 16.75 310.57 196.39 305.25 301.23 0.4062E+01 0.4689E+01 0.1497E+01 0.3690E+01 ----------------------------------------------------------------------------------------------------------------------------





A.4 – 116


: :


1) 2)

tt = 0.3750" gt’= 2.0000" rt = 3.5000" ps = 2.3750" nt’= 2 X 1 2

6.5000" 3.6250" 2.5000"

ns = 2 X

ls = gs = qs = 1

0.3750" 2.0000" 3.5000"

ns’= 2 X

ts = gs’= rs =

IV - 59

------------------------------

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------26 774.19 46.08 27 781.78 48.71


= 6.5000" = 3.6250" = 2.5000" = 2.3750" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A.




Tested by Test Id.


0

95

190

285

380

475

570

665

760

855

950

0

column

8

pt

24

ps gs'

qs

qt

rs ls

lt rt

32

40

48

56

64

72


beam

gt'


16

gs

gt

80

ts

tt

A.4 – 117


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.51628781E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1376E+03 0.4659E+02 0.1033E+03 0.1031E+03 2 0.46 62.72 20.57 57.56 47.01 0.1373E+03 0.4245E+02 0.1405E+03 0.1031E+03 3 0.86 117.60 36.26 114.75 88.34 0.1287E+03 0.3575E+02 0.1416E+03 0.1031E+03 4 1.22 161.27 48.13 163.98 125.50 0.1252E+03 0.3037E+02 0.1305E+03 0.1031E+03 5 1.59 209.41 58.59 209.59 163.90 0.1163E+03 0.2600E+02 0.1141E+03 0.1031E+03 6 2.10 259.77 70.72 261.88 216.70 0.8652E+02 0.2163E+02 0.9043E+02 0.1031E+03 7 2.78 307.85 84.00 313.89 286.70 0.6802E+02 0.1773E+02 0.6404E+02 0.1028E+03 8 3.52 355.96 96.00 353.48 358.44 0.5429E+02 0.1490E+02 0.4444E+02 0.7947E+02 9 4.74 400.66 112.18 396.20 387.73 0.3096E+02 0.1193E+02 0.2841E+02 0.9777E+00 10 6.11 434.14 126.99 430.08 387.97 0.2148E+02 0.9859E+01 0.2217E+02 0.5916E-02 11 7.87 465.33 142.80 465.72 387.98 0.1593E+02 0.8155E+01 0.1829E+02 0.3529E-04 12 9.96 494.26 158.34 498.90 387.98 0.1197E+02 0.6853E+01 0.1351E+02 0.3105E-06 13 12.20 516.45 172.56 523.98 387.98 0.1080E+02 0.5904E+01 0.9224E+01 0.5200E-08 14 14.12 538.67 183.30 539.71 387.98 0.1088E+02 0.5306E+01 0.7453E+01 0.2725E-09 15 16.68 564.19 196.07 558.39 387.98 0.9882E+01 0.4702E+01 0.7492E+01 0.9480E-11 16 19.40 590.82 208.17 580.52 387.98 0.8779E+01 0.4217E+01 0.8855E+01 0.4514E-12 17 22.43 614.05 220.32 609.54 387.98 0.8330E+01 0.3800E+01 0.1011E+02 0.2408E-13 18 25.39 640.65 231.07 639.98 387.98 0.8453E+01 0.3478E+01 0.1028E+02 0.1983E-14 19 28.03 661.68 239.92 666.35 387.98 0.8025E+01 0.3242E+01 0.9609E+01 0.2706E-15 20 30.91 684.92 248.93 692.24 387.98 0.7481E+01 0.3025E+01 0.8322E+01 0.3776E-16 21 33.62 703.71 256.90 712.92 387.98 0.6092E+01 0.2850E+01 0.6897E+01 0.6915E-17 22 36.34 718.01 264.42 729.71 387.98 0.5776E+01 0.2698E+01 0.5494E+01 0.1447E-17 23 38.81 733.45 270.95 741.85 387.98 0.6583E+01 0.2576E+01 0.4343E+01 0.3833E-18 24 41.21 750.02 276.99 751.08 387.98 0.6361E+01 0.2470E+01 0.3389E+01 0.1146E-18 25 43.68 764.34 282.98 758.43 387.98 0.4938E+01 0.2370E+01 0.2576E+01 0.3537E-19 26 46.08 774.19 288.54 763.81 387.98 0.3529E+01 0.2283E+01 0.1948E+01 0.1207E-19 27 48.71 781.78 294.43 768.20 387.98 0.2883E+01 0.2196E+01 0.1413E+01 0.3943E-20 ----------------------------------------------------------------------------------------------------------------------------

Power model : rn =19.155




A.4 – 118


: :


Remark

lt gt qt pt nt

1) 2)

tt = 0.3750" gt’= 2.0000" rt = 3.5000" ps = 2.3750" nt’= 2 X 1 2

6.5000" 3.6250" 2.5000"

ns = 2 X

ls = gs = qs =

Major parameters

1

0.3750" 2.0000" 3.5000"

ns’= 2 X

ts = gs’= rs =

IV - 60



= 6.5000" = 3.6250" = 2.5000" = 2.3750" = 2 X 2

U.S.A.




Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

pt

ps

beam

gs'

gt'

11

33

44

55

66


22


gs

gt

88

qs

qt

99

rs ls

lt rt

110

ts

tt

A.4 – 119


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.59566842E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1385E+03 0.4659E+02 0.1344E+03 0.1031E+03 2 0.72 99.39 31.12 98.49 74.02 0.1325E+03 0.3809E+02 0.1347E+03 0.1031E+03 3 1.22 163.79 48.23 163.08 125.77 0.1228E+03 0.3032E+02 0.1216E+03 0.1031E+03 4 1.75 225.37 62.55 222.43 180.04 0.1034E+03 0.2449E+02 0.1037E+03 0.1031E+03 5 2.41 282.71 77.14 283.68 248.77 0.7520E+02 0.1964E+02 0.8042E+02 0.1031E+03 6 3.31 337.25 92.86 343.62 339.38 0.5716E+02 0.1558E+02 0.5390E+02 0.9149E+02 7 4.22 386.08 105.75 383.45 384.83 0.4434E+02 0.1301E+02 0.3508E+02 0.1159E+02 8 6.49 433.45 130.70 434.98 387.97 0.1902E+02 0.9419E+01 0.1531E+02 0.6570E-02 9 8.76 472.41 149.76 465.77 387.98 0.1470E+02 0.7532E+01 0.1302E+02 0.3266E-04 10 12.36 511.22 173.58 512.64 387.98 0.1053E+02 0.5843E+01 0.1248E+02 0.7356E-07 11 15.86 547.24 192.17 551.01 387.98 0.8767E+01 0.4876E+01 0.9260E+01 0.8934E-09 12 19.77 574.82 209.72 580.78 387.98 0.7445E+01 0.4160E+01 0.6362E+01 0.1814E-10 13 23.98 607.96 226.06 605.70 387.98 0.7769E+01 0.3623E+01 0.5859E+01 0.5925E-12 14 28.30 641.09 240.79 632.94 387.98 0.7697E+01 0.3220E+01 0.6853E+01 0.3162E-13 15 32.41 672.84 253.40 663.13 387.98 0.6749E+01 0.2925E+01 0.7745E+01 0.2864E-14 16 36.73 697.57 265.47 697.28 387.98 0.5834E+01 0.2678E+01 0.7940E+01 0.3134E-15 17 41.35 725.06 277.34 732.83 387.98 0.5900E+01 0.2464E+01 0.7318E+01 0.3842E-16 18 46.28 753.92 289.01 766.06 387.98 0.5813E+01 0.2276E+01 0.6097E+01 0.5228E-17 19 50.08 775.90 297.43 787.21 387.98 0.5883E+01 0.2154E+01 0.5032E+01 0.1293E-17 20 53.99 799.27 305.62 804.78 387.98 0.5941E+01 0.2044E+01 0.3985E+01 0.3423E-18 21 57.48 819.89 312.60 817.22 387.98 0.5050E+01 0.1956E+01 0.3154E+01 0.1128E-18 22 61.08 834.89 319.49 827.21 387.98 0.3181E+01 0.1875E+01 0.2430E+01 0.3856E-19 23 63.85 841.59 324.68 833.28 387.98 0.1911E+01 0.1817E+01 0.1963E+01 0.1758E-19 24 69.08 846.60 333.85 841.67 387.98 0.9587E+00 0.1721E+01 0.1282E+01 0.4361E-20 ----------------------------------------------------------------------------------------------------------------------------





A.4 – 120


: :


1) 2)

tt = 0.3750" gt’= 2.0000" rt = 3.5000" ps = 2.3750" nt’= 2 X 1 2

6.5000" 3.6250" 2.5000"

ns = 2 X

ls = gs = qs = 1

0.3750" 2.0000" 3.5000"

ns’= 2 X

ts = gs’= rs =

IV - 61


column

------------------------------



= 6.5000" = 3.6250" = 2.5000" = 2.3750" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

U.S.A.




Tested by Test Id.


Moment ( kip-inch )

0

65

130

195

260

325

390

455

520

585

650

0

gs

gt

10

pt

30

rs ls

qs

qt

40

50

60

70

80

90


gs'


20

ps

beam

gt'

lt rt

100

ts

tt

A.4 – 121


R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.97379111E+04

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1067E+03 0.4659E+02 0.1157E+03 0.1031E+03 3 0.29 30.72 13.24 29.66 29.43 0.1067E+03 0.4478E+02 0.9217E+02 0.1007E+03 5 0.60 55.17 26.70 56.15 60.50 0.6296E+02 0.4001E+02 0.7664E+02 0.9530E+02 7 1.06 86.54 43.18 88.13 101.65 0.6855E+02 0.3258E+02 0.6544E+02 0.8518E+02 9 1.70 130.52 61.39 127.76 151.22 0.5937E+02 0.2493E+02 0.5954E+02 0.6993E+02 11 2.33 164.68 75.53 164.44 191.02 0.5306E+02 0.2012E+02 0.5638E+02 0.5619E+02 13 3.21 208.61 91.24 211.59 233.44 0.5324E+02 0.1595E+02 0.5033E+02 0.4101E+02 15 4.12 256.03 104.37 253.29 265.19 0.4088E+02 0.1326E+02 0.4150E+02 0.2984E+02 17 6.76 296.90 133.21 294.15 318.13 0.8498E+01 0.9134E+01 0.1363E+02 0.1304E+02 19 10.56 315.91 162.40 317.66 349.75 0.4792E+01 0.6561E+01 0.3004E+01 0.5164E+01 21 14.41 334.92 184.85 332.23 363.74 0.5417E+01 0.5228E+01 0.4865E+01 0.2526E+01 23 18.26 351.13 203.26 352.45 371.07 0.3903E+01 0.4405E+01 0.5132E+01 0.1428E+01 25 22.19 366.63 219.40 369.00 375.50 0.4586E+01 0.3829E+01 0.3067E+01 0.8807E+00 27 24.45 367.70 227.75 372.29 377.26 0.1730E+03 0.3573E+01 -0.2079E+01 0.6910E+00 29 25.37 392.03 231.03 390.73 377.86 0.1203E+02 0.3479E+01 0.1983E+02 0.6296E+00 31 28.58 410.44 241.70 409.15 379.60 0.5590E+01 0.3197E+01 0.4933E+01 0.4653E+00 33 31.61 419.78 251.10 422.34 380.84 0.3333E+01 0.2976E+01 0.3858E+01 0.3599E+00 35 34.73 431.90 260.10 433.22 381.84 0.2761E+01 0.2784E+01 0.3173E+01 0.2828E+00 37 38.30 442.56 269.71 443.72 382.73 0.2950E+01 0.2598E+01 0.2762E+01 0.2199E+00 39 41.87 453.22 278.69 453.22 383.43 0.2843E+01 0.2441E+01 0.2591E+01 0.1747E+00 41 45.49 461.07 287.24 462.47 384.00 0.4187E+01 0.2303E+01 0.2543E+01 0.1410E+00 43 48.38 470.43 293.71 469.83 384.38 0.2689E+01 0.2207E+01 0.2547E+01 0.1202E+00 45 51.04 477.03 299.53 476.64 384.67 0.2168E+01 0.2125E+01 0.2565E+01 0.1046E+00 47 54.16 484.96 305.97 484.67 384.98 0.1897E+01 0.2039E+01 0.2590E+01 0.8963E-01 49 57.73 494.22 313.17 493.96 385.27 0.2953E+01 0.1949E+01 0.2617E+01 0.7591E-01 51 61.07 500.02 319.50 502.74 385.51 0.8204E+00 0.1875E+01 0.2637E+01 0.6556E-01 ----------------------------------------------------------------------------------------------------------------------------





A.4 – 122


: :


tt = 0.4646" gt’= 2.3622" rt = 4.1339" nt’= 2 X 1

ls gs qs ns

= 7.0866" = 2.3622" = -" = 2 X 1

ts = 0.4646" gs’= 2.3622" rs = 4.1339" ns’= 2 X 1

IV - 62

------------------------------


1) Elastic and Plastic moments of beam are Me,b = 144 kNm, Mp,b = 172 kNm. 2)

= 7.0866" = 2.3622" = -" = 2 X 1

Major parameters


Remark

lt gt qt nt

Italy

Fasteners: G8.8- -M20 7/8" Oversize holes Material : A36 Fy = 45.40 ksi Fu = 66.57 ksi

C. Bernuzzi et al. (1996) TSC/M

Column : -Beam : IPE300 Angle : L120x120x12

Tested by Test Id.


0

85

170

255

340

425

510

595

680

765

850

0

column

12

pt

36

ps gs'

qs

qt

rs ls

lt rt

48

60

72

84

96

ts

tt

108 120


beam

gt'


24

gs

gt

A.4 – 123


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.14931887E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1234E+03 0.9902E+02 0.2056E+03 0.2140E+03 3 1.52 187.93 120.69 179.42 150.44 0.9061E+02 0.5678E+02 0.6188E+02 0.6113E+02 5 3.01 235.48 186.90 241.52 221.44 0.1289E+02 0.3556E+02 0.3021E+02 0.3775E+02 7 5.02 241.67 245.41 242.92 282.09 0.2522E+01 0.2427E+02 -0.2596E+00 0.2436E+02 9 7.03 261.92 288.21 269.61 323.64 0.2549E+02 0.1886E+02 0.2707E+02 0.1762E+02 11 9.03 317.86 322.49 317.51 354.57 0.1566E+02 0.1566E+02 0.2041E+02 0.1361E+02 13 11.04 350.55 351.66 350.87 379.07 0.1889E+02 0.1350E+02 0.1292E+02 0.1094E+02 15 13.05 375.10 377.15 370.59 399.08 0.4191E+01 0.1194E+02 0.7069E+01 0.9065E+01 17 16.06 381.03 410.43 383.94 423.23 0.2235E+01 0.1027E+02 0.2626E+01 0.7118E+01 19 20.08 392.19 448.45 392.56 448.20 0.3809E+01 0.8743E+01 0.2381E+01 0.5435E+01 21 24.09 405.31 481.26 405.89 467.64 0.1533E+01 0.7675E+01 0.4343E+01 0.4332E+01 23 28.11 408.26 510.43 407.68 483.42 0.4882E+01 0.6876E+01 0.7001E+00 0.3558E+01 25 32.12 451.37 536.71 447.97 496.49 0.7145E+01 0.6256E+01 0.1027E+02 0.2991E+01 27 36.14 477.45 560.83 476.11 507.61 0.1064E+02 0.5756E+01 0.6863E+01 0.2560E+01 29 40.15 494.68 583.26 502.56 517.18 0.3479E+01 0.5342E+01 0.6290E+01 0.2224E+01 31 44.17 527.41 604.00 526.49 525.56 0.9071E+01 0.4996E+01 0.5617E+01 0.1955E+01 33 48.18 550.44 623.42 547.77 532.95 0.9860E+00 0.4701E+01 0.5016E+01 0.1737E+01 35 52.20 566.49 641.78 566.95 539.56 0.4088E+01 0.4445E+01 0.4551E+01 0.1556E+01 37 56.21 586.98 659.13 584.51 545.48 0.6761E+01 0.4221E+01 0.4230E+01 0.1404E+01 39 60.23 604.42 675.59 601.07 550.86 0.2387E+01 0.4024E+01 0.4029E+01 0.1275E+01 41 64.24 613.93 691.54 616.98 555.75 0.6129E+01 0.3845E+01 0.3919E+01 0.1165E+01 43 68.26 637.30 706.59 632.62 560.23 0.1115E+01 0.3687E+01 0.3871E+01 0.1069E+01 45 72.27 644.67 721.22 648.12 564.35 0.5461E+01 0.3542E+01 0.3862E+01 0.9862E+00 47 76.29 666.01 735.05 663.66 568.16 0.4296E+01 0.3413E+01 0.3874E+01 0.9131E+00 49 79.30 674.34 745.26 675.35 570.84 0.9351E+00 0.3322E+01 0.3891E+01 0.8641E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.91083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.15450686E+04 -0.12910879E+05 0.45054691E+05 -0.71754475E+05 0.53469773E+05 Rj0 = 3.0100 6.0600 28.1100 24.4500 32.1200 RKj = -0.26454511E+02 0.30030566E+02 0.89656311E+01 -0.52458960E+01 -0.32302575E+01



A.4 – 124


: :


tt = 0.3661" gt’= 2.3386" rt = 3.3622" nt’= 2 X 1

ls gs qs ns

= 5.7165" = 2.3386" = 2.7953" = 2 X 1

ts = 0.3661" gs’= 2.3386" rs = 3.3622" ns’= 2 X 1

IV - 63

------------------------------


1) Plastic moment of beam: Mp,b = 90.2 kNm. Failure mode: local buckling of beam. 2) Max. axial force of beam at Nmax=118.36 kN

= 5.7165" = 2.3386" = 2.7953" = 2 X 1


Remark

lt gt qt nt

Japan Fasteners: F10T- -M20 7/8" Oversize holes Material : SS400 Fy = 44.16 ksi Fu = 65.57 ksi

Major parameters

N. Kubo et al. (1999) No.1


Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

pt

ps

beam

gs'

gt'

18

54

72

90

qs

qt

rs ls

lt rt

ts

tt

108 126 144 162 180 Rotation ( x 1/1000 radians )

36


gs

gt

A.4 – 125


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.11237926E+06

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.6353E+02 0.5753E+02 0.4679E+02 0.5714E+02 3 2.25 104.38 91.21 109.55 123.95 0.3189E+02 0.2547E+02 0.4125E+02 0.4895E+02 5 5.71 193.91 151.92 185.49 220.60 0.1911E+02 0.1280E+02 0.5581E+01 0.1091E+02 7 11.16 255.43 205.29 255.90 241.16 0.1093E+02 0.7781E+01 0.8880E+01 0.9342E+00 9 16.02 297.28 238.25 299.69 243.42 0.7810E+01 0.5979E+01 0.9179E+01 0.2106E+00 11 21.07 339.11 265.52 344.40 244.04 0.9989E+01 0.4908E+01 0.8377E+01 0.6679E-01 13 25.55 392.26 286.01 380.75 244.24 -0.2818E+02 0.4276E+01 0.8083E+01 0.2965E-01 15 28.24 332.87 297.10 331.43 244.31 -0.7325E+01 0.3983E+01 -0.1796E+02 0.1944E-01 17 34.22 304.19 319.32 309.93 244.39 -0.4200E+01 0.3476E+01 -0.1653E+01 0.8636E-02 19 43.52 311.86 348.96 314.61 244.44 0.1389E+02 0.2935E+01 0.4127E+01 0.3126E-02 21 46.85 393.28 358.61 381.65 244.44 0.2623E+02 0.2785E+01 0.2118E+02 0.2289E-02 23 52.49 446.33 373.58 449.08 244.46 0.5831E+01 0.2574E+01 0.7506E+01 0.1415E-02 25 58.90 496.50 389.51 502.16 244.46 0.1159E+02 0.2374E+01 0.8792E+01 0.8694E-03 27 64.55 552.37 402.53 552.29 244.47 0.8822E+01 0.2227E+01 0.8814E+01 0.5902E-03 29 70.57 599.75 415.53 603.53 244.47 0.8735E+01 0.2093E+01 0.8123E+01 0.4047E-03 31 73.47 579.79 421.40 579.03 244.47 -0.6650E+02 0.2036E+01 -0.7696E+02 0.3413E-03 33 80.47 641.17 435.20 645.91 244.47 0.6827E+01 0.1911E+01 0.8886E+01 0.2323E-03 35 86.69 696.99 446.93 697.52 244.47 0.9213E+01 0.1814E+01 0.7725E+01 0.1695E-03 37 91.74 727.56 455.81 734.35 244.47 0.6348E+01 0.1745E+01 0.6877E+01 0.1334E-03 39 95.05 769.54 461.55 756.28 244.47 0.1799E+02 0.1702E+01 0.6382E+01 0.1148E-03 41 104.56 816.63 477.30 811.23 244.48 0.4326E+01 0.1593E+01 0.5244E+01 0.7672E-04 43 115.03 852.37 493.40 861.48 244.48 0.2710E+01 0.1491E+01 0.4421E+01 0.5124E-04 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.11910833E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = -0.11924016E+04 0.20886304E+05 -0.11536080E+06 0.27726870E+06 -0.29366365E+06 Rj0 = 5.7100 25.5500 28.2400 34.2200 43.5200 48.8000 72.9100 73.4700 RKj = 0.17502401E+02 -0.26677727E+02 0.12822062E+02 -0.15467006E+01 0.14889746E+02 -0.16233923E+02 -0.84599901E+02 0.87162728E+02



A.4 – 126


: :


tt = 0.3622" gt’= 2.3819" rt = 3.3661" nt’= 2 X 1

ls gs qs ns

= 5.7126" = 2.3819" = 2.8150" = 2 X 1

ts = 0.3622" gs’= 2.3819" rs = 3.3661" ns’= 2 X 1

IV - 64

------------------------------



= 5.7126" = 2.3819" = 2.8150" = 2 X 1


Remark

lt gt qt nt


Major parameters



Tested by Test Id.


0

95

190

285

380

475

570

665

760

855

950

0

column

28

pt

84

ps gs'

qs

qt

rs ls

lt rt

ts

tt

112 140 168 196 224 252 280


beam

gt'


56

gs

gt

A.4 – 127


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.35835709E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4570E+02 0.5720E+02 0.5896E+02 0.5077E+02 3 1.93 84.45 82.13 82.08 93.60 0.3319E+02 0.2814E+02 0.2968E+02 0.4325E+02 5 4.36 135.00 132.00 132.86 170.14 0.1524E+02 0.1559E+02 0.1440E+02 0.2021E+02 7 11.71 194.42 208.25 191.81 219.96 0.7454E+01 0.7468E+01 0.6719E+01 0.1562E+01 9 20.09 252.18 259.11 251.58 225.63 0.7725E+01 0.5048E+01 0.7484E+01 0.2579E+00 11 31.34 320.16 307.20 324.02 227.03 0.5130E+01 0.3677E+01 0.5410E+01 0.5555E-01 13 42.93 383.08 345.19 381.05 227.41 0.4186E+01 0.2946E+01 0.4138E+01 0.1857E-01 15 50.61 390.07 366.52 388.97 227.52 -0.5957E+01 0.2625E+01 -0.3984E+01 0.1045E-01 17 55.53 361.45 379.02 366.51 227.56 0.3072E+01 0.2460E+01 -0.5151E+01 0.7557E-02 19 60.36 415.72 390.55 401.46 227.60 0.3232E+00 0.2321E+01 0.6678E+01 0.5646E-02 21 63.80 424.28 398.46 423.13 227.61 0.1829E+02 0.2232E+01 0.5928E+01 0.4651E-02 23 67.81 446.39 407.15 445.27 227.63 0.2175E+01 0.2140E+01 0.5133E+01 0.3758E-02 25 72.98 471.91 418.08 469.47 227.65 0.7484E+01 0.2032E+01 0.4258E+01 0.2907E-02 27 83.18 504.34 437.74 506.16 227.67 0.2509E+01 0.1857E+01 0.3047E+01 0.1839E-02 29 97.51 540.27 462.90 543.43 227.69 0.2260E+01 0.1663E+01 0.2309E+01 0.1054E-02 31 111.73 577.89 485.44 575.30 227.70 0.2755E+01 0.1514E+01 0.2245E+01 0.6548E-03 33 128.93 618.98 510.20 615.93 227.71 0.2602E+01 0.1371E+01 0.2506E+01 0.3966E-03 35 145.67 661.75 532.19 660.39 227.72 0.2418E+01 0.1260E+01 0.2800E+01 0.2587E-03 37 166.77 719.87 557.54 722.54 227.72 0.3115E+01 0.1148E+01 0.3069E+01 0.1611E-03 39 186.60 788.25 579.42 784.97 227.72 0.3758E+01 0.1062E+01 0.3213E+01 0.1087E-03 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18050000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = 0.64644953E+03 -0.67793173E+04 0.38550901E+05 -0.94110393E+05 0.98029810E+05 Rj0 = 1.9300 4.3600 25.2600 47.8600 55.5300 RKj = 0.32595528E+00 -0.11257062E+01 -0.23085068E+01 -0.64938775E+01 0.12955286E+02



A.4 – 128


: :


tt = 0.2992" gt’= 2.7717" rt = 2.9921" pt’= 1.5827" nt’= 2 X 2

ls gs qs ps ns

= 5.4094" = 2.7717" = 3.0551" = 1.5827" = 2 X 2

ts = 0.2992" gs’= 2.7717" rs = 2.9921" ps’= 1.5827" ns’= 2 X 2

IV - 65

------------------------------



= 5.4094" = 2.7717" = 3.0551" = 1.5827" = 2 X 2


Remark

lt gt qt pt nt


Major parameters



Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

column

pt

ps

beam

gs'

gt'

20

60

80

qs

qt

rs ls

lt rt

ts

tt

100 120 140 160 180 200 Rotation ( x 1/1000 radians )

40


gs

gt

A.4 – 129


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.76201123E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4033E+02 0.3915E+02 0.4231E+02 0.4732E+02 3 1.52 60.78 47.69 63.05 71.67 0.3963E+02 0.2246E+02 0.3883E+02 0.4652E+02 5 4.10 147.84 87.50 145.23 170.80 0.2317E+02 0.1117E+02 0.2540E+02 0.2538E+02 7 9.39 227.66 129.73 224.95 214.13 0.1602E+02 0.6010E+01 0.1493E+02 0.1332E+01 9 14.96 290.81 157.69 286.32 216.91 0.8475E+01 0.4274E+01 0.8489E+01 0.1455E+00 11 21.89 353.83 183.36 361.77 217.34 0.1301E+02 0.3249E+01 0.1191E+02 0.2283E-01 13 28.24 437.15 202.15 433.02 217.42 0.1150E+02 0.2710E+01 0.1013E+02 0.6579E-02 15 32.30 410.77 212.66 432.93 217.44 -0.4913E+02 0.2463E+01 -0.2957E+02 0.3412E-02 17 36.56 375.70 222.67 375.75 217.45 0.7854E+00 0.2257E+01 0.2719E+01 0.1862E-02 19 43.88 427.12 238.15 432.10 217.46 0.1486E+02 0.1985E+01 0.1267E+02 0.7629E-03 21 49.10 389.07 248.11 383.30 217.46 -0.6809E+01 0.1835E+01 -0.2271E+02 0.4403E-03 23 54.89 403.03 258.32 411.00 217.46 0.3389E+01 0.1697E+01 0.3334E+01 0.2552E-03 25 59.51 448.90 265.96 439.88 217.47 0.2113E+02 0.1604E+01 0.1537E+02 0.1719E-03 27 64.31 509.22 273.44 508.31 217.47 0.1375E+02 0.1520E+01 0.1317E+02 0.1176E-03 29 71.05 586.72 283.33 587.57 217.47 0.9547E+01 0.1418E+01 0.1042E+02 0.7225E-04 31 79.13 658.33 294.36 660.33 217.47 0.7622E+01 0.1316E+01 0.7703E+01 0.4267E-04 33 90.11 732.57 308.16 729.25 217.47 0.6259E+01 0.1202E+01 0.5035E+01 0.2260E-04 35 99.76 751.98 319.40 769.93 217.47 0.6202E+01 0.1120E+01 0.3506E+01 0.1374E-04 37 103.80 783.44 323.90 783.13 217.47 0.3352E+01 0.1090E+01 0.3041E+01 0.1132E-04 39 110.36 806.61 330.84 801.06 217.47 0.4069E+01 0.1045E+01 0.2458E+01 0.8385E-05 41 117.11 822.22 337.82 816.13 217.47 0.2291E+01 0.1002E+01 0.2032E+01 0.6272E-05 43 127.15 821.90 347.57 834.31 217.47 -0.2517E+01 0.9470E+00 0.1625E+01 0.4195E-05 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12245833E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = -0.54862691E+03 0.98489462E+04 -0.53183809E+05 0.13712546E+06 -0.16762922E+06 Rj0 = 4.1000 11.8800 31.3100 34.4300 40.2200 45.8000 49.1000 58.2000 RKj = -0.54513855E+01 -0.14192974E+02 -0.37801305E+02 0.34419161E+02 0.13650850E+02 -0.32742595E+02 0.28956803E+02 0.14272473E+02



A.4 – 130


: :


tt = 0.3071" gt’= 2.7697" rt = 3.0039" pt’= 1.5472" nt’= 2 X 2

ls gs qs ps ns

= 5.4055" = 2.7697" = 3.0276" = 1.5472" = 2 X 2

ts = 0.3071" gs’= 2.7697" rs = 3.0039" ps’= 1.5472" ns’= 2 X 2

IV - 66


1) Plastic moment of beam: Mp,b = 90.2 kNm. Failure mode: bolt fracture 2) Max. axial force of beam at Nmax=79.32 kN

= 5.4055" = 2.7697" = 3.0276" = 1.5472" = 2 X 2


Remark

lt gt qt pt nt


Major parameters



Tested by Test Id.


0

90

180

270

360

450

540

630

720

810

900

0

column

22

pt

66

ps gs'

qs

qt

rs ls

lt rt

88

ts

tt

110 132 154 176 198 220


beam

gt'


44

gs

gt

A.4 – 131


Moment ( kip-inch )

R f A3 P3

© 2011 J. Ross Publishing, Inc. Q3 =


0.96111921E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3759E+02 0.3964E+02 0.3416E+02 0.4976E+02 3 2.45 83.26 66.24 83.53 113.82 0.2771E+02 0.1652E+02 0.2795E+02 0.3881E+02 5 4.90 143.65 97.08 145.97 180.07 0.2058E+02 0.9892E+01 0.2270E+02 0.1661E+02 7 7.83 187.48 121.18 185.80 208.57 0.1153E+02 0.6967E+01 0.6493E+01 0.5176E+01 9 17.17 245.06 168.80 241.12 223.88 0.5574E+01 0.3916E+01 0.6284E+01 0.3893E+00 11 27.93 312.24 203.84 313.70 225.74 0.6500E+01 0.2765E+01 0.6043E+01 0.6886E-01 13 40.39 389.02 233.92 384.84 226.20 0.7419E+01 0.2131E+01 0.6671E+01 0.1823E-01 15 48.17 448.63 249.48 450.58 226.30 0.4661E+01 0.1883E+01 0.1050E+02 0.9649E-02 17 56.47 479.14 264.25 479.55 226.36 0.5766E+01 0.1685E+01 0.5860E+01 0.5431E-02 19 60.34 447.92 270.71 436.16 226.38 -0.3981E+02 0.1608E+01 -0.4684E+02 0.4273E-02 21 61.61 370.35 272.75 377.06 226.39 -0.1187E+03 0.1585E+01 -0.4625E+02 0.3963E-02 23 65.64 430.17 278.92 436.11 226.40 0.2035E+02 0.1517E+01 0.1545E+02 0.3151E-02 25 68.90 491.98 283.83 488.31 226.41 -0.2089E+03 0.1466E+01 0.1653E+02 0.2644E-02 27 69.27 445.46 284.37 412.82 226.41 0.2290E+04 0.1461E+01 -0.2040E+03 0.2593E-02 29 71.07 393.05 287.00 400.96 226.41 0.1791E+02 0.1435E+01 0.2253E+02 0.2363E-02 31 73.29 462.67 290.17 451.57 226.42 0.4777E+02 0.1404E+01 0.2304E+02 0.2114E-02 33 76.03 524.51 293.87 515.42 226.43 0.5413E+02 0.1370E+01 0.2354E+02 0.1851E-02 35 78.11 565.07 296.71 564.71 226.43 0.1219E+02 0.1344E+01 0.2384E+02 0.1679E-02 37 85.50 584.02 306.32 591.28 226.44 0.3217E+01 0.1263E+01 0.3814E+01 0.1210E-02 39 94.70 628.04 317.61 626.56 226.45 0.4263E+01 0.1176E+01 0.3752E+01 0.8360E-03 41 102.87 660.50 326.92 655.67 226.45 0.3235E+01 0.1110E+01 0.3341E+01 0.6195E-03 43 113.10 688.97 337.85 686.50 226.46 0.1765E+01 0.1040E+01 0.2681E+01 0.4395E-03 45 121.26 702.06 346.24 706.28 226.46 0.3245E+01 0.9905E+00 0.2176E+01 0.3415E-03 47 129.56 726.76 354.22 722.46 226.47 0.2161E+01 0.9465E+00 0.1737E+01 0.2687E-03 49 139.36 738.94 363.22 737.40 226.47 -0.4005E+00 0.9003E+00 0.1332E+01 0.2063E-03 ----------------------------------------------------------------------------------------------------------------------------


-1

) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 0.00000000E+00 Nexp= 6 Nliner= 8 -0.12087614E+06 0.27199169E+06 -0.26932260E+06 48.1700 59.0600 61.6100 78.1100 -0.94202616E+01 -0.54681558E+02 0.60043476E+02 -0.20580131E+02


( R : X 1/1000 radians )

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) C = 0.15018333E+01 Bmo= AI = -0.13091695E+04 0.23103518E+05 Rj0 = 3.6300 7.8300 68.9000 69.5000 RKj = 0.15129953E+02 0.45704082E+01 -0.22061243E+03 0.22601436E+03



A.4 – 132


: :


tt = 0.3150" gt’= 2.7638" rt = 3.0315" pt’= 1.5748" nt’= 2 X 2

ls gs qs ps ns

= 5.4016" = 2.7638" = 3.0315" = 1.5748" = 2 X 2

ts = 0.3150" gs’= 2.7638" rs = 3.0315" ps’= 1.5748" ns’= 2 X 2

IV - 67

------------------------------


1) Plastic moment of beam: Mp,b = 90.2 kNm. Failure mode: bolt fracture 2)

= 5.4016" = 2.7638" = 3.0315" = 1.5748" = 2 X 2


Remark

lt gt qt pt nt


Major parameters


Column : H175x175x7.5x11 Beam : H250x125x6x9 Angle : L120x120x8

Tested by Test Id.


0

75

150

225

300

375

450

525

600

675

750

0

column

24

pt

72

ps gs'

qs

qt

rs ls

lt rt

96

ts

tt

120 144 168 192 216 240


beam

gt'


48

gs

gt

A.4 – 133


Moment ( kip-inch )

R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.43341618E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5076E+02 0.4012E+02 0.6039E+02 0.5652E+02 3 1.62 76.50 51.14 78.47 87.17 0.4201E+02 0.2213E+02 0.3803E+02 0.4827E+02 5 3.53 137.07 82.79 134.02 159.42 0.2036E+02 0.1281E+02 0.2163E+02 0.2751E+02 7 7.08 180.14 117.19 182.32 214.01 0.1011E+02 0.7600E+01 0.8258E+01 0.7585E+01 9 21.39 253.92 186.25 256.74 240.77 0.3834E+01 0.3386E+01 0.4535E+01 0.3187E+00 11 36.30 306.60 227.63 303.20 242.93 0.2315E+01 0.2325E+01 0.2033E+01 0.6008E-01 13 49.16 327.86 254.41 329.75 243.41 0.2438E+01 0.1879E+01 0.2399E+01 0.2285E-01 15 61.74 366.46 276.19 366.00 243.61 0.3567E+01 0.1603E+01 0.3287E+01 0.1103E-01 17 68.86 387.36 287.17 390.23 243.68 0.2768E+01 0.1485E+01 0.3470E+01 0.7776E-02 19 78.64 423.72 301.04 423.69 243.74 0.3639E+01 0.1354E+01 0.3304E+01 0.5082E-02 21 89.78 458.73 315.43 457.64 243.78 0.1533E+01 0.1235E+01 0.2750E+01 0.3324E-02 23 101.62 457.71 329.55 459.18 243.82 0.2290E+01 0.1133E+01 0.4146E+01 0.2235E-02 25 112.08 500.49 340.98 499.48 243.84 0.2818E+01 0.1059E+01 0.3576E+01 0.1632E-02 27 122.70 535.55 351.89 534.90 243.85 0.2361E+01 0.9946E+00 0.3114E+01 0.1221E-02 29 130.93 550.26 359.85 546.94 243.86 0.1628E+01 0.9512E+00 0.1332E+01 0.9916E-03 31 141.40 557.06 369.50 559.47 243.87 0.6231E+01 0.9022E+00 0.1077E+01 0.7748E-03 33 147.40 596.44 374.88 597.95 243.87 0.2110E+01 0.8765E+00 0.6363E+01 0.6781E-03 35 153.91 594.25 380.54 594.10 243.88 -0.5473E+01 0.8505E+00 -0.9226E+01 0.5903E-03 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.15430833E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = -0.88223043E+02 0.62656791E+04 -0.39073844E+05 0.98471247E+05 -0.10837527E+06 Rj0 = 89.7800 101.6000 122.7000 141.4000 147.4000 153.9000 RKj = -0.22705036E+01 0.43785016E+01 -0.15082720E+01 0.53934246E+01 -0.68943041E+01 -0.86030961E+01



A.4 – 134


: :


tt = 0.4724" gt’= 2.1654" rt = 4.7244" ps = 2.1654" nt’= 2 X 1

IV - 68

1

column

------------------------------


0.4724" 2.1654" 4.7244"

ns’= 2 X

ts = gs’= rs =


2

7.8740" 3.2480" 4.7244"

ns = 2 X

ls = gs = qs =

1) Failure mode: Bolt fracture 2) Original T & S angles: L150x100x15

= 7.8740" = 3.2480" = 4.7244" = 2.1654" = 2 X 2

Major parameters


Remark

lt gt qt pt nt

Japan



Column : -Beam : H400x200x8x13 Angle : L150x100x12

Tested by Test Id.


Moment ( kip-inch )

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

gs

gt

17

pt

ps

51

68

85

rs ls

qs ts

tt


34

gs'

qt


beam

gt'

lt rt

A.4 – 135


R f A3 P3

( R : X 1/1000 radians ) = Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.787400" xl = 7.874020" = 1.240000 K = 0.007142 = 5 Q1 = -1 Q2 = -1

Q3 =



0.59744923E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.6591E+03 0.1655E+03 0.5808E+03 0.6547E+03 3 0.51 270.79 81.15 238.19 219.33 0.3198E+03 0.1477E+03 0.3667E+03 0.3116E+03 5 1.01 392.31 147.58 383.43 346.29 0.1615E+03 0.1184E+03 0.2237E+03 0.2088E+03 7 1.50 457.30 199.72 468.56 434.23 0.1437E+03 0.9571E+02 0.1303E+03 0.1548E+03 9 3.01 546.65 312.39 554.06 601.71 0.3579E+02 0.5943E+02 0.1479E+02 0.8048E+02 11 5.01 580.77 409.78 577.66 721.77 0.6904E+01 0.4063E+02 0.2181E+02 0.4512E+02 13 6.98 573.29 480.14 580.75 793.76 0.4902E+01 0.3169E+02 0.1771E+02 0.2971E+02 15 9.02 612.94 538.75 606.20 844.75 0.1570E+02 0.2619E+02 0.1998E+02 0.2108E+02 17 12.02 654.53 609.21 667.90 896.40 0.1293E+02 0.2120E+02 0.1665E+02 0.1410E+02 19 16.01 699.69 685.15 684.98 941.95 -0.1431E+02 0.1721E+02 -0.9216E+01 0.9271E+01 21 20.00 685.72 748.38 681.24 973.20 0.2639E+02 0.1466E+02 0.2822E+02 0.6629E+01 23 23.98 757.20 802.97 765.03 996.13 0.1400E+02 0.1287E+02 0.1547E+02 0.5012E+01 25 28.00 811.15 851.88 815.16 1013.97 0.1326E+02 0.1153E+02 0.1047E+02 0.3933E+01 27 31.97 859.56 895.51 854.38 1028.03 0.1294E+02 0.1049E+02 0.9745E+01 0.3188E+01 29 36.03 907.97 936.32 895.63 1039.79 0.4390E+01 0.9642E+01 0.1070E+02 0.2634E+01 31 40.04 944.36 973.90 940.98 1049.48 0.1590E+02 0.8946E+01 0.1189E+02 0.2222E+01 33 43.98 991.81 1007.95 989.56 1057.60 0.1224E+02 0.8376E+01 0.1269E+02 0.1908E+01 35 48.00 1044.77 1040.57 1041.32 1064.74 0.1397E+02 0.7878E+01 0.1298E+02 0.1654E+01 37 52.04 1094.48 1071.50 1093.57 1070.99 0.1016E+02 0.7446E+01 0.1282E+02 0.1449E+01 39 55.98 1131.52 1100.06 1143.20 1076.37 0.1130E+02 0.7076E+01 0.1234E+02 0.1285E+01 41 60.03 1189.36 1127.85 1191.86 1081.28 0.1029E+02 0.6741E+01 0.1167E+02 0.1145E+01 43 64.02 1223.48 1154.45 1236.97 1085.61 0.1474E+02 0.6443E+01 0.1094E+02 0.1029E+01 45 67.99 1272.54 1179.34 1278.96 1089.50 0.7365E+01 0.6180E+01 0.1022E+02 0.9313E+00 47 71.99 1321.31 1203.81 1318.47 1093.05 0.1098E+02 0.5937E+01 0.9548E+01 0.8467E+00 49 76.03 1357.66 1227.10 1355.81 1096.32 0.1162E+02 0.5718E+01 0.8951E+01 0.7729E+00 51 80.08 1392.76 1250.04 1391.00 1099.31 0.9578E+01 0.5514E+01 0.8441E+01 0.7086E+00 53 83.97 1427.19 1270.84 1423.02 1101.96 0.8117E+01 0.5338E+01 0.8034E+01 0.6544E+00 55 88.00 1459.39 1292.18 1454.68 1104.50 0.7560E+01 0.5166E+01 0.7691E+01 0.6048E+00 57 92.02 1488.65 1312.78 1485.03 1106.84 0.7528E+01 0.5007E+01 0.7418E+01 0.5610E+00 59 95.98 1514.59 1332.46 1513.96 1108.98 0.6430E+01 0.4862E+01 0.7205E+01 0.5225E+00 61 99.99 1544.48 1351.30 1542.50 1111.01 0.5023E+01 0.4729E+01 0.7037E+01 0.4877E+00 63 103.99 1574.08 1370.09 1570.38 1112.90 0.5322E+01 0.4601E+01 0.6908E+01 0.4564E+00 65 108.00 1585.45 1388.42 1597.88 1114.67 0.4100E+01 0.4482E+01 0.6809E+01 0.4281E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.98191667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.38292850E+04 -0.81827185E+04 -0.30450376E+05 0.12478900E+06 -0.14800970E+06 Rj0 = 5.0100 6.9800 16.0100 18.0100 RKj = -0.37568114E+02 -0.16156171E+02 -0.19106488E+02 0.79344558E+02



A.4 – 136


: :


tt = 0.5906" gt’= 2.3622" rt = 4.7244" ps = 3.5433" nt’= 2 X 1

IV - 69

1

column

------------------------------


0.5906" 2.3622" 4.7244"

ns’= 2 X

ts = gs’= rs =


2

7.8740" 4.1339" 4.7244"

ns = 2 X

ls = gs = qs =


= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2


Remark

lt gt qt pt nt


Major parameters

Y. Sato et al. (2007) G60


Tested by Test Id.


Moment ( kip-inch )

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

gs

gt

14

pt

ps

42

56

70

84

98

rs ls

qs ts

tt


28

gs'

qt


beam

gt'

lt rt

A.4 – 137


R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.30006035E+04

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1133E+04 0.1850E+03 0.9280E+03 0.9345E+03 3 0.50 409.17 89.08 362.97 275.98 0.4335E+03 0.1658E+03 0.5526E+03 0.3891E+03 5 1.01 563.36 165.00 579.25 436.97 0.2303E+03 0.1324E+03 0.3154E+03 0.2595E+03 7 2.02 739.81 273.82 767.24 636.76 0.1213E+03 0.8826E+02 0.9765E+02 0.1532E+03 9 4.00 883.76 408.36 863.14 854.23 0.5721E+02 0.5378E+02 0.3500E+02 0.8014E+02 11 6.02 954.46 500.90 944.41 983.32 0.3174E+02 0.3958E+02 0.4285E+02 0.5131E+02 13 8.01 1008.97 571.45 1017.98 1069.50 0.1752E+02 0.3198E+02 0.2766E+02 0.3668E+02 15 10.00 1034.49 629.95 1047.59 1133.12 0.8140E+01 0.2713E+02 0.1918E+01 0.2792E+02 17 14.02 1055.77 725.88 1055.51 1223.19 0.8130E+01 0.2118E+02 0.8567E+01 0.1807E+02 19 17.64 1084.40 796.28 1082.75 1279.21 -0.2294E+03 0.1794E+02 0.9971E+01 0.1329E+02 21 18.38 898.66 809.46 893.46 1288.77 -0.1722E+03 0.1741E+02 -0.2546E+03 0.1256E+02 23 22.00 1093.40 868.37 1093.05 1328.91 0.5583E+02 0.1530E+02 0.8985E+02 0.9802E+01 25 26.02 1187.29 926.25 1209.04 1363.91 0.2227E+02 0.1358E+02 0.3511E+02 0.7741E+01 27 30.00 1262.73 977.58 1253.16 1391.73 0.1603E+02 0.1227E+02 0.1431E+02 0.6317E+01 29 34.04 1328.23 1024.95 1317.42 1415.01 0.1538E+02 0.1122E+02 0.1684E+02 0.5263E+01 31 38.02 1387.83 1067.88 1384.27 1434.33 0.1466E+02 0.1038E+02 0.1643E+02 0.4478E+01 33 42.01 1441.27 1107.86 1446.69 1450.93 0.1294E+02 0.9676E+01 0.1475E+02 0.3867E+01 35 46.02 1498.31 1145.42 1501.84 1465.42 0.1239E+02 0.9076E+01 0.1276E+02 0.3378E+01 37 50.01 1541.76 1180.59 1549.05 1478.08 0.1037E+02 0.8563E+01 0.1096E+02 0.2984E+01 39 54.00 1572.37 1213.84 1589.75 1489.32 0.9046E+01 0.8115E+01 0.9505E+01 0.2659E+01 41 58.01 1616.40 1245.97 1625.55 1499.42 0.9754E+01 0.7715E+01 0.8411E+01 0.2387E+01 43 61.98 1655.77 1275.68 1657.31 1508.44 0.9574E+01 0.7369E+01 0.7635E+01 0.2160E+01 45 65.99 1691.49 1304.43 1686.77 1516.69 0.9195E+01 0.7056E+01 0.7094E+01 0.1963E+01 47 70.00 1725.76 1332.43 1714.44 1524.22 0.8169E+01 0.6769E+01 0.6729E+01 0.1795E+01 49 73.99 1756.81 1358.65 1740.78 1531.08 0.7431E+01 0.6516E+01 0.6490E+01 0.1649E+01 51 77.97 1782.69 1384.34 1766.28 1537.39 0.5445E+01 0.6281E+01 0.6335E+01 0.1521E+01 53 82.01 1802.90 1409.49 1791.65 1543.30 0.3516E+01 0.6063E+01 0.6234E+01 0.1408E+01 55 86.08 1811.22 1433.43 1816.88 1548.82 0.4147E-01 0.5865E+01 0.6170E+01 0.1306E+01 57 89.99 1800.03 1456.19 1840.93 1553.75 -0.4569E+01 0.5686E+01 0.6132E+01 0.1220E+01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.81241667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.61244397E+04 -0.41941031E+05 0.11853589E+06 -0.13825958E+06 0.59534420E+05 Rj0 = 12.0000 17.6400 18.3800 20.0200 22.0000 26.0200 RKj = 0.38906246E+02 -0.26688608E+03 0.26962832E+03 0.60784672E+02 -0.68154121E+02 -0.28209955E+02



A.4 – 138


: :


tt = 0.5906" gt’= 4.1339" rt = 4.7244" ps = 3.5433" nt’= 2 X 1

IV - 70

1

column

------------------------------


0.5906" 4.1339" 4.7244"

ns’= 2 X

ts = gs’= rs =


2

7.8740" 4.1339" 4.7244"

ns = 2 X

ls = gs = qs =


= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2


Remark

lt gt qt pt nt


Major parameters

Y. Sato et al. (2007) G105


Tested by Test Id.


Moment ( kip-inch )

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

gs

gt

25

pt

ps

75

rs ls

qs ts

tt

100 125 150 175 200 225 250 Rotation ( x 1/1000 radians )

50

gs'

qt


beam

gt'

lt rt

A.4 – 139


R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



0.32665411E+04

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2300E+03 0.1850E+03 0.2437E+03 0.9256E+02 3 0.51 117.54 90.73 110.20 47.20 0.2017E+03 0.1652E+03 0.1905E+03 0.9254E+02 5 1.00 199.86 163.68 193.24 92.51 0.1467E+03 0.1330E+03 0.1500E+03 0.9234E+02 7 2.01 310.44 272.92 312.70 184.99 0.9335E+02 0.8856E+02 0.9130E+02 0.9032E+02 9 4.00 425.90 408.36 428.97 351.69 0.3452E+02 0.5378E+02 0.3501E+02 0.7414E+02 11 6.99 484.47 537.34 489.02 511.23 0.1382E+02 0.3538E+02 0.1136E+02 0.3349E+02 13 12.02 538.30 681.21 522.72 591.08 0.9624E+01 0.2369E+02 0.1670E+02 0.6036E+01 15 19.99 607.56 836.59 615.16 610.16 0.7458E+01 0.1639E+02 0.7262E+01 0.7704E+00 17 28.02 662.50 952.70 661.09 613.32 0.6837E+01 0.1288E+02 0.5520E+01 0.1834E+00 19 36.02 716.17 1046.73 716.74 614.20 0.4026E+01 0.1078E+02 0.8717E+01 0.6241E-01 21 44.00 731.04 1126.80 726.03 614.53 0.3951E+01 0.9367E+01 0.2769E+01 0.2637E-01 23 52.01 777.10 1197.48 782.05 614.68 0.7538E+01 0.8331E+01 0.7896E+01 0.1282E-01 25 60.02 845.76 1260.90 849.22 614.76 0.8317E+01 0.7538E+01 0.8713E+01 0.6914E-02 27 68.01 918.32 1318.53 919.55 614.80 0.9323E+01 0.6909E+01 0.8811E+01 0.4032E-02 29 76.02 994.89 1371.75 989.37 614.82 0.8766E+01 0.6395E+01 0.8594E+01 0.2494E-02 31 83.99 1052.99 1420.96 1056.68 614.84 0.7273E+01 0.5967E+01 0.8294E+01 0.1622E-02 33 92.01 1116.65 1467.31 1112.81 614.85 0.9027E+01 0.5601E+01 0.5712E+01 0.1094E-02 35 100.00 1177.36 1510.78 1157.52 614.86 -0.1638E+03 0.5287E+01 0.5489E+01 0.7639E-03 37 102.01 954.09 1521.37 932.75 614.86 -0.6473E+01 0.5215E+01 0.4188E+02 0.7010E-03 39 106.01 1094.67 1542.09 1099.80 614.86 0.2432E+02 0.5077E+01 0.1049E+02 0.5938E-03 41 114.01 1182.13 1581.52 1183.16 614.87 0.9883E+01 0.4828E+01 0.1036E+02 0.4338E-03 43 122.00 1267.15 1619.64 1265.58 614.87 0.1016E+02 0.4605E+01 0.1028E+02 0.3238E-03 45 130.00 1346.76 1655.45 1347.55 614.87 0.1030E+02 0.4408E+01 0.1022E+02 0.2462E-03 47 138.02 1425.23 1690.43 1429.36 614.87 0.9105E+01 0.4228E+01 0.1018E+02 0.1901E-03 49 146.02 1488.45 1723.24 1499.75 614.88 0.6410E+01 0.4068E+01 -0.5974E+00 0.1491E-03 51 153.61 1516.98 1753.85 1495.16 614.88 -0.3484E-01 0.3927E+01 -0.6117E+00 0.1198E-03 53 160.00 1497.60 1778.78 1491.23 614.88 -0.1552E+02 0.3818E+01 -0.6198E+00 0.1005E-03 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.14119167E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = 0.18488477E+04 -0.10399070E+05 0.27634051E+05 -0.26642622E+05 0.47190750E+04 Rj0 = 12.0000 36.0200 44.0000 88.0000 100.0000 102.0000 106.0000 145.0000 RKj = 0.13546827E+02 -0.93339015E+01 0.30832937E+01 -0.23017097E+01 -0.11805826E+03 0.15449713E+03 -0.31313582E+02 -0.10757177E+02



A.4 – 140


: :


tt = 0.5906" gt’= 5.9055" rt = 4.7244" ps = 3.5433" nt’= 2 X 1

IV - 71

1

column

------------------------------


0.5906" 5.9055" 4.7244"

ns’= 2 X

ts = gs’= rs =


2

7.8740" 4.1339" 4.7244"

ns = 2 X

ls = gs = qs =

1) Original T & S angles: L200x200x20 2)

= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2


Remark

lt gt qt pt nt


Major parameters

Y. Sato et al. (2007) G150


Tested by Test Id.


Moment ( kip-inch )

0

150

300

450

600

750

900

1050

1200

1350

1500

0

gs

gt

26

pt

ps

78

rs ls

qs ts

tt


52

gs'

qt


beam

gt'

lt rt

A.4 – 141


R f A3 P3



0.15937328E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1546E+03 0.1850E+03 0.1257E+03 0.2513E+02 3 0.50 67.18 89.08 57.47 12.57 0.1015E+03 0.1658E+03 0.1048E+03 0.2513E+02 5 1.51 141.32 224.44 145.76 37.95 0.6696E+02 0.1065E+03 0.7196E+02 0.2513E+02 7 3.01 227.48 349.26 227.84 75.65 0.4650E+02 0.6645E+02 0.4025E+02 0.2513E+02 9 5.00 288.41 457.69 285.55 125.66 0.1947E+02 0.4549E+02 0.2054E+02 0.2513E+02 11 9.98 332.91 629.66 335.60 250.81 0.6342E+01 0.2715E+02 0.5037E+01 0.2513E+02 13 17.99 374.28 802.58 372.27 354.24 0.4378E+01 0.1768E+02 0.4782E+01 0.3564E-01 15 26.02 406.35 926.26 408.16 354.26 0.3686E+01 0.1358E+02 0.3871E+01 0.1754E-05 17 33.99 436.77 1024.40 433.29 354.26 0.3732E+01 0.1123E+02 0.2532E+01 0.1332E-08 19 41.99 467.89 1107.66 468.65 354.26 0.4523E+01 0.9679E+01 0.4247E+01 0.4536E-11 21 50.02 504.04 1180.67 503.27 354.26 0.4604E+01 0.8562E+01 0.4453E+01 0.4108E-13 23 57.99 538.99 1245.42 540.52 354.26 -0.3169E+01 0.7721E+01 0.4904E+01 0.7718E-15 25 64.00 533.40 1290.24 528.24 354.26 0.3117E+01 0.7208E+01 0.8213E+00 0.5448E-16 27 71.98 579.44 1345.42 581.78 354.26 0.7541E+01 0.6642E+01 0.6840E+01 0.2314E-17 29 80.01 638.33 1397.27 637.33 354.26 0.6944E+01 0.6167E+01 0.6973E+01 0.1347E-18 31 87.99 692.13 1444.83 693.09 354.26 0.6672E+01 0.5774E+01 0.6986E+01 0.1046E-19 33 95.98 747.72 1489.55 748.71 354.26 0.7033E+01 0.5437E+01 0.6929E+01 0.1011E-20 35 104.00 803.01 1531.93 803.93 354.26 0.6924E+01 0.5144E+01 0.6840E+01 0.1169E-21 37 112.02 858.22 1572.11 858.40 354.26 0.7034E+01 0.4886E+01 0.6744E+01 0.1587E-22 39 120.00 915.41 1609.93 911.87 354.26 0.6704E+01 0.4660E+01 0.6658E+01 0.2495E-23 41 127.99 966.57 1646.75 964.76 354.26 0.5486E+01 0.4455E+01 0.6585E+01 0.4411E-24 43 133.35 929.53 1669.92 934.62 354.26 0.1237E+02 0.4332E+01 -0.4185E+02 0.1464E-24 45 136.01 996.15 1681.41 997.59 354.26 0.1576E+02 0.4274E+01 0.5172E+01 0.8609E-25 47 141.99 986.32 1706.80 984.91 354.26 -0.1924E+02 0.4147E+01 -0.1673E+02 0.2708E-25 49 146.02 974.04 1723.43 968.38 354.26 0.1375E+02 0.4068E+01 0.8460E+01 0.1276E-25 51 153.99 1038.13 1754.92 1035.68 354.26 0.7879E+01 0.3923E+01 0.8430E+01 0.3058E-26 53 162.00 1100.03 1786.06 1103.11 354.26 0.7928E+01 0.3786E+01 0.8408E+01 0.7823E-27 55 169.76 1169.53 1815.20 1168.30 354.26 0.9459E+01 0.3665E+01 0.8393E+01 0.2224E-27 ----------------------------------------------------------------------------------------------------------------------------


-1

) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 0.00000000E+00 Nexp= 6 Nliner= 10 -0.20282495E+05 0.45567403E+05 -0.44556145E+05 57.9900 60.0000 64.0000 136.0000 140.0000 144.0000 -0.12508825E+02 0.81095544E+01 0.57292255E+01 -0.19824867E+02 -0.21864440E+02 0.25205777E+02


( R : X 1/1000 radians )

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) C = 0.14771667E+01 Bmo= AI = 0.28832471E+03 0.34139463E+04 Rj0 = 4.0100 33.9900 132.0000 133.4000 RKj = 0.28305317E+01 0.22124109E+01 -0.48390871E+02 0.66861062E+02



A.4 – 142


: :


tt = 0.5906" gt’= 4.1339" rt = 4.7244" pt’= 3.5433" nt’= 2 X 2

ls gs qs ps ns

= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2

IV - 72 column

------------------------------


ts = 0.5906" gs’= 4.1339" rs = 4.7244" ps’= 3.5433" ns’= 2 X 2



= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2


Remark

lt gt qt pt nt


Major parameters

Y. Sato et al. (2007) GW60


Tested by Test Id.


Moment ( kip-inch )

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

gs

gt

ps

beam

gs'

30

90

rs ls

qs

qt

ts

tt


60


pt

gt'

lt rt

A.4 – 143


R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.18819098E+06

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.6986E+03 0.1850E+03 0.5779E+03 0.9345E+03 3 0.50 268.45 89.08 250.92 212.89 0.3842E+03 0.1658E+03 0.4318E+03 0.2828E+03 5 1.00 439.11 163.68 437.29 327.79 0.2802E+03 0.1330E+03 0.3186E+03 0.1900E+03 7 2.01 669.61 272.92 674.52 476.19 0.1677E+03 0.8856E+02 0.1658E+03 0.1160E+03 9 4.01 846.39 408.89 856.78 647.58 0.5641E+02 0.5368E+02 0.4525E+02 0.6478E+02 11 8.00 994.80 571.23 1003.85 829.92 0.3115E+02 0.3200E+02 0.4792E+02 0.3306E+02 13 14.00 1128.56 725.66 1140.14 975.18 0.1490E+02 0.2119E+02 0.2104E+02 0.1804E+02 15 19.99 1010.25 836.55 1010.25 1062.87 0.3837E+01 0.1639E+02 -0.8949E+02 0.1197E+02 17 25.99 1272.98 925.86 1290.22 1124.12 0.1892E+02 0.1359E+02 0.1886E+02 0.8743E+01 19 34.01 1409.49 1024.62 1400.08 1183.43 0.1462E+02 0.1123E+02 0.1379E+02 0.6281E+01 21 40.02 1386.30 1088.65 1387.54 1217.48 -0.3377E+02 0.1000E+02 -0.3676E+02 0.5121E+01 23 43.99 1382.37 1127.02 1402.24 1236.62 0.3914E+02 0.9363E+01 0.4387E+02 0.4541E+01 25 51.99 1568.25 1197.32 1549.77 1269.23 0.1288E+02 0.8333E+01 0.1218E+02 0.3665E+01 27 59.99 1667.57 1260.68 1661.63 1295.93 0.1252E+02 0.7541E+01 0.1486E+02 0.3043E+01 29 67.99 1767.11 1318.39 1776.47 1318.34 0.1199E+02 0.6911E+01 0.1339E+02 0.2582E+01 31 75.99 1861.04 1371.56 1871.71 1337.53 0.1166E+02 0.6396E+01 0.1032E+02 0.2229E+01 33 84.01 1949.84 1421.08 1942.01 1354.24 0.9404E+01 0.5966E+01 0.7297E+01 0.1950E+01 35 92.02 1979.91 1467.37 1990.38 1368.93 -0.4815E+01 0.5601E+01 -0.1507E+02 0.1726E+01 37 101.71 1829.82 1520.02 1833.02 1384.56 -0.1818E+03 0.5224E+01 -0.2929E+03 0.1508E+01 39 106.29 486.80 1543.77 490.65 1391.26 -0.2133E+03 0.5066E+01 -0.2933E+03 0.1421E+01 41 116.01 584.49 1591.36 584.85 1404.27 0.1201E+02 0.4769E+01 0.9952E+01 0.1261E+01 43 126.01 696.56 1637.47 685.43 1416.19 0.1045E+02 0.4506E+01 0.1022E+02 0.1127E+01 45 134.02 779.19 1673.17 768.70 1424.84 0.1014E+02 0.4316E+01 0.1058E+02 0.1036E+01 47 142.01 862.48 1706.60 854.84 1432.79 0.1089E+02 0.4148E+01 0.1098E+02 0.9563E+00 49 150.02 946.05 1739.51 944.31 1440.16 0.9882E+01 0.3993E+01 0.1135E+02 0.8867E+00 51 157.99 1029.11 1771.05 1036.14 1446.98 0.1133E+02 0.3851E+01 0.1168E+02 0.8255E+00 53 166.00 1131.44 1800.94 1130.83 1453.37 0.1087E+02 0.3724E+01 0.1195E+02 0.7709E+00 55 173.99 1209.44 1830.45 1227.24 1459.33 0.1160E+02 0.3604E+01 0.1217E+02 0.7222E+00 57 182.00 1305.66 1859.09 1325.43 1464.94 0.1247E+02 0.3493E+01 0.1234E+02 0.6783E+00 59 190.00 1452.48 1886.17 1424.69 1470.21 0.2026E+02 0.3392E+01 0.1247E+02 0.6389E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.16781667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 10 AI = 0.12266980E+05 -0.11668683E+06 0.43451023E+06 -0.74717843E+06 0.60669605E+06 Rj0 = 8.0000 18.0000 20.0000 22.0000 38.0000 42.0000 46.0000 92.0000 101.7000 106.3000 RKj = -0.38186888E+02 -0.68939772E+02 0.18357869E+03 -0.44816276E+02 -0.59358014E+02 0.74190477E+02 -0.40714248E+02 -0.20100143E+02 -0.27625754E+03 0.30342047E+03



A.4 – 144


: :


tt = 0.5906" gt’= 2.3622" rt = 4.7244" ps = 3.5433" nt’= 2 X 1

IV - 73

1

column

------------------------------


0.5906" 2.3622" 4.7244"

ns’= 2 X

ts = gs’= rs =


2

7.8740" 4.1339" 4.7244"

ns = 2 X

ls = gs = qs =


= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2


Remark

lt gt qt pt nt


Major parameters

Y. Sato et al. (2007) A40


Tested by Test Id.


Moment ( kip-inch )

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

gs

gt

14

pt

ps

42

56

70

84

98

rs ls

qs ts

tt


28

gs'

qt


beam

gt'

lt rt

A.4 – 145


R f A3 P3


( R : X 1/1000 radians )

-1

Q3 =



-0.19669285E+05

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5768E+03 0.1850E+03 0.5936E+03 0.9345E+03 3 0.51 257.65 90.73 254.54 260.53 0.4163E+03 0.1652E+03 0.4155E+03 0.3521E+03 5 1.00 415.88 163.68 427.22 401.59 0.2616E+03 0.1330E+03 0.2964E+03 0.2386E+03 7 1.99 641.35 271.14 641.93 583.15 0.1600E+03 0.8916E+02 0.1545E+03 0.1434E+03 9 4.01 826.05 408.90 826.37 791.46 0.5196E+02 0.5368E+02 0.5255E+02 0.7570E+02 11 6.02 897.00 500.90 902.21 914.10 0.2943E+02 0.3958E+02 0.2799E+02 0.4955E+02 13 7.99 952.06 570.81 948.07 997.25 0.2328E+02 0.3204E+02 0.1965E+02 0.3609E+02 15 10.01 985.87 630.22 982.89 1061.05 0.1264E+02 0.2711E+02 0.1524E+02 0.2771E+02 17 14.01 1028.90 725.67 1034.68 1151.04 0.1060E+02 0.2119E+02 0.1143E+02 0.1836E+02 19 17.99 1076.13 802.52 1077.40 1213.23 0.1183E+02 0.1768E+02 0.1016E+02 0.1334E+02 21 22.02 1121.14 868.68 1115.69 1260.28 -0.1424E+02 0.1529E+02 0.8726E+01 0.1024E+02 23 26.01 1146.11 926.11 1143.11 1296.79 0.3418E+02 0.1358E+02 0.4930E+02 0.8189E+01 25 30.01 1213.83 977.70 1211.38 1326.49 0.1571E+02 0.1227E+02 0.1594E+02 0.6741E+01 27 34.01 1268.56 1024.62 1271.04 1351.22 0.1335E+02 0.1123E+02 0.1396E+02 0.5674E+01 29 38.01 1321.01 1067.78 1323.79 1372.22 0.1254E+02 0.1038E+02 0.1250E+02 0.4860E+01 31 42.02 1369.03 1107.95 1371.88 1390.38 0.1177E+02 0.9674E+01 0.1156E+02 0.4221E+01 33 46.00 1415.08 1145.24 1416.76 1406.13 0.1161E+02 0.9079E+01 0.1105E+02 0.3714E+01 35 49.99 1463.87 1180.42 1460.34 1420.10 0.1148E+02 0.8565E+01 0.1083E+02 0.3299E+01 37 54.01 1507.46 1213.92 1503.76 1432.64 0.1027E+02 0.8114E+01 0.1079E+02 0.2953E+01 39 58.02 1543.53 1246.05 1547.15 1443.89 -0.1394E+02 0.7714E+01 0.1086E+02 0.2664E+01 41 62.02 1498.76 1275.98 1494.70 1454.04 0.1330E+02 0.7366E+01 0.1389E+02 0.2419E+01 43 66.02 1550.85 1304.64 1550.49 1463.29 0.1232E+02 0.7054E+01 0.1401E+02 0.2209E+01 45 69.98 1593.98 1332.29 1593.27 1471.67 0.9635E+01 0.6771E+01 0.7599E+01 0.2029E+01 47 74.02 1625.39 1358.84 1624.17 1479.54 0.6329E+01 0.6514E+01 0.7691E+01 0.1869E+01 49 77.98 1640.70 1384.40 1642.08 1486.66 0.8514E+00 0.6281E+01 0.1322E+01 0.1732E+01 51 82.00 1639.26 1409.43 1636.76 1493.37 -0.1833E+01 0.6063E+01 -0.4051E+01 0.1608E+01 53 84.02 1631.53 1421.62 1628.61 1496.56 -0.6014E+01 0.5961E+01 -0.4027E+01 0.1551E+01 55 88.00 1590.08 1444.60 1590.08 1502.53 -0.1304E+02 0.5776E+01 -0.2262E+04 0.1449E+01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.79333333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 9 AI = 0.15745252E+04 -0.75277842E+04 0.32435955E+05 -0.65473053E+05 0.59828878E+05 Rj0 = 22.0200 24.0100 26.0100 58.0200 60.2000 68.0000 76.0100 80.0200 87.9900 RKj = -0.44586288E+02 0.87236427E+02 -0.31090774E+02 -0.46519103E+02 0.49448742E+02 -0.65112762E+01 -0.64425099E+01 -0.54302668E+01 -0.22580333E+04



A.4 – 146


: :


tt = 0.5906" gt’= 2.3622" rt = 4.7244" ps = 3.5433" nt’= 2 X 1

IV - 74

1

column

------------------------------


0.5906" 2.3622" 4.7244"

ns’= 2 X

ts = gs’= rs =


2

7.8740" 4.1339" 4.7244"

ns = 2 X

ls = gs = qs =


= 7.8740" = 4.1339" = 4.7244" = 3.5433" = 2 X 2


Remark

lt gt qt pt nt


Major parameters

Y. Sato et al. (2007) A90


Tested by Test Id.


Moment ( kip-inch )

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

gs

gt

15

pt

ps

45

60

75

90

rs ls

qs ts

tt

105 120 135 150 Rotation ( x 1/1000 radians )

30

gs'

qt


beam

gt'

lt rt

A.4 – 147


R f A3 P3

( R : X 1/1000 radians )



0.27656606E+06

-5

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.7532E+03 0.1850E+03 0.6655E+03 0.9345E+03 3 0.50 292.73 89.08 278.67 252.85 0.3970E+03 0.1658E+03 0.4609E+03 0.3484E+03 5 1.00 460.96 163.68 471.02 394.52 0.2980E+03 0.1330E+03 0.3170E+03 0.2338E+03 7 1.99 696.14 271.14 691.87 572.62 0.1632E+03 0.8916E+02 0.1499E+03 0.1408E+03 9 4.02 845.28 409.44 855.17 778.47 0.4909E+02 0.5358E+02 0.4209E+02 0.7455E+02 11 6.00 921.97 500.11 920.74 898.04 0.3476E+02 0.3968E+02 0.2913E+02 0.4929E+02 13 8.01 991.26 571.45 977.03 982.29 0.2446E+02 0.3198E+02 0.2655E+02 0.3578E+02 15 10.01 1022.33 630.22 1024.50 1045.10 0.1301E+02 0.2711E+02 0.2032E+02 0.2763E+02 17 14.01 1061.93 725.67 1075.36 1135.01 0.9296E+01 0.2119E+02 0.6327E+01 0.1838E+02 19 18.02 1105.03 803.05 1094.10 1197.80 0.1158E+02 0.1766E+02 0.5673E+01 0.1338E+02 21 21.53 1136.00 861.12 1129.60 1239.61 -0.3215E+03 0.1554E+02 0.1569E+02 0.1062E+02 23 22.61 744.26 877.76 747.73 1250.71 -0.1642E+03 0.1500E+02 -0.3515E+03 0.9960E+01 25 26.01 1142.68 926.11 1159.20 1281.56 0.5817E+02 0.1358E+02 0.1276E+03 0.8270E+01 27 30.02 1220.45 977.82 1216.29 1311.65 0.1701E+02 0.1226E+02 0.8992E+01 0.6818E+01 29 34.01 1280.78 1024.62 1267.99 1336.63 0.1499E+02 0.1123E+02 0.1592E+02 0.5751E+01 31 38.00 1345.16 1067.68 1335.84 1357.88 0.1566E+02 0.1038E+02 0.1725E+02 0.4936E+01 33 41.98 1405.20 1107.57 1416.44 1376.21 0.1523E+02 0.9681E+01 0.1852E+02 0.4298E+01 35 46.00 1462.73 1145.24 1480.39 1392.41 0.1347E+02 0.9079E+01 0.1299E+02 0.3781E+01 37 50.02 1515.90 1180.67 1519.30 1406.73 0.1272E+02 0.8562E+01 0.6275E+01 0.3360E+01 39 52.98 1549.16 1205.79 1530.34 1416.28 -0.2181E+03 0.8220E+01 0.1197E+01 0.3097E+01 41 56.01 1308.14 1229.94 1305.73 1425.30 0.9510E+02 0.7911E+01 0.9390E+02 0.2861E+01 43 59.99 1533.41 1261.05 1532.78 1436.14 0.1872E+02 0.7536E+01 0.2067E+02 0.2594E+01 45 63.98 1597.48 1290.25 1604.83 1446.02 0.1425E+02 0.7208E+01 0.1559E+02 0.2365E+01 47 68.01 1648.47 1318.99 1658.85 1455.13 0.1228E+02 0.6905E+01 0.1137E+02 0.2165E+01 49 72.02 1693.19 1345.82 1697.47 1463.46 0.8817E+01 0.6638E+01 0.8023E+01 0.1993E+01 51 76.01 1725.42 1372.06 1724.07 1471.11 0.7770E+01 0.6392E+01 0.5423E+01 0.1843E+01 53 79.99 1751.09 1396.69 1741.51 1478.18 0.5668E+01 0.6173E+01 0.3433E+01 0.1711E+01 55 84.01 1769.40 1421.29 1752.12 1484.82 0.2656E+01 0.5964E+01 0.1915E+01 0.1593E+01 57 88.02 1773.22 1445.01 1757.42 1490.99 -0.9028E+00 0.5773E+01 0.7880E+00 0.1488E+01 59 91.99 1763.19 1467.20 1758.83 1496.71 -0.4073E+01 0.5602E+01 -0.3584E-01 0.1395E+01 61 96.00 1736.91 1489.50 1757.40 1502.13 -0.1330E+02 0.5438E+01 -0.6447E+00 0.1310E+01 ----------------------------------------------------------------------------------------------------------------------------


-1

) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 0.00000000E+00 Nexp= 6 Nliner= 8 -0.15860621E+06 0.50987380E+06 -0.63989072E+06 26.0100 28.0200 38.0000 57.9900 -0.10901728E+03 -0.22268161E+02 0.41668650E+01 -0.67286583E+02


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) C = 0.86650000E+00 Bmo= AI = 0.18062051E+04 0.13262517E+05 Rj0 = 21.5300 22.6100 52.9800 53.9600 RKj = -0.37130263E+03 0.46584234E+03 -0.42945318E+03 0.52714131E+03



A.4 – 148


: :

© 2011 J. Ross Publishing, Inc. pc =

3.5000"

------------------------------


End plate extended on tension and compression sides.


1) 2)

End plate extended on both sides. ct = 1.6250" pt = 3.5000" li = 10.2500" cc = 1.6250" gt = 5.5000" gc = 5.5000" tp = 0.6250" nt = 2 X 2 nc = 2 X 2

Remark

U.S.A. Fasteners: A325- -3/4"D 13/16" Oversize holes Material : A36 Fy = -ksi Fu = -ksi

Major parameters

S.A.Ioannides (1978) TEST 1

Column : W8x35 Beam : W14x22 Plate thickness : 5/8"

Tested by Test Id.

V -

1

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )

Connection type : Extended end-plate connections Mode : All bolted without column stiffener

0

4

12

16

cc

pc

li

pt

ct

24

28

32

: A36 Experimental Polynominal M. Exponential

20

Material : : :

gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 1


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3



Frye and Morris polynominal model : xd = 17.250000" t = 0.625000" A1 = 1.830000 A2 = -1.040000 P1 = 1 P2 = 3


A.5 – 2


: :


3.7500"

------------------------------


End plate extended on tension and compression sides.


1) 2)


Remark


Major parameters



Tested by Test Id.

V -

2

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

4

12

16

cc

pc

li

pt

ct

24

28

32


20

Material : : :

gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 3


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 4


: :


4.0000"

------------------------------


End plate extended on tension and compression side.


1) 2)


Remark

U.S.A. Fasteners: A325- -1"D 1 1/16" Oversize holes Material : A36 Fy = -ksi Fu = -ksi

Major parameters



Tested by Test Id.

V -

3

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

2

6

8

cc

pc

li

pt

ct

12

14

16


10

Material : : :

gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 5


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 6


: :


3.5000"

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V -

4

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

7

21

28

cc

pc

li

pt

ct

42

49

56


35

Material : : :

gc


14

beam

gt

63

lp

70

nc

ni

nt

A.5 – 7


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 8


: :


3.7500"

------------------------------




1) 2)


Remark


Major parameters


Column : W10x49 Beam : W18x35 Plate thickness : 1 1/4"

Tested by Test Id.

V -

5

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

li

pt

ct

36

42

48


30

Material : : :

gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 9


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 10


: :


4.0000"

------------------------------




1) 2)


Remark

U.S.A. Fasteners: A325- -1"D 1 1/16" Oversize holes Material : A36 Fy = -ksi Fu = -ksi

Major parameters



Tested by Test Id.

V -

6

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

2

6

8

cc

pc

li

pt

ct

12

14

16


10

Material : : :

gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 11


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 12


: :


3.5000"

------------------------------




1) 2)


Remark

U.S.A. Fasteners: A325- -3/4"D 15/16" Oversize holes Material : A36 Fy = 48.10 ksi Fu = -ksi

Major parameters

R.J.Dews (1979) TEST 1

Column : W8x31 Beam : W14x22 Plate thickness : 1"

Tested by Test Id.

V -

7

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

cc

pc

li

pt

ct

96

Material : A36 Fy = 48.10 ksi : Experimental : Polynominal : M. Exponential

gc


24

beam

gt

nc

ni

108 120

lp

nt

A.5 – 13


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 14


: :


3.5000"

------------------------------




1) 2)


Remark

U.S.A. Fasteners: A325- -3/4"D 15/16" Oversize holes Material : A36 Fy = 36.90 ksi Fu = -ksi

Major parameters



Tested by Test Id.

V -

8

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

10

30

40

50

60

70

cc

pc

li

pt

ct

80


gc


20

beam

gt

90

lp

100

nc

ni

nt

A.5 – 15


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 16


: :


1) 2)

pc =

3.7500"




Remark

U.S.A. Fasteners: A325- -1"D 1 1/4" Oversize holes Material : A36 Fy = 42.30 ksi Fu = -ksi

Major parameters



Tested by Test Id.

V -

9

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

li

pt

ct

20

25

30

35

40


gc


10

beam

gt

45

lp

50

nc

ni

nt

A.5 – 17


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1736E+04 0.8133E+03 0.6981E+03 2 0.50 868.22 408.39 868.14 0.1169E+04 0.8238E+03 0.1598E+04 3 1.36 1031.43 1146.36 1031.94 0.1310E+03 0.8987E+03 0.9910E+02 4 2.34 1095.29 2115.06 1094.00 0.5166E+02 0.1119E+04 0.4425E+02 5 3.37 1133.49 3440.67 1134.60 0.3721E+02 0.1386E+04 0.3751E+02 6 4.39 1171.70 4607.41 1172.47 0.3721E+02 0.8410E+03 0.3609E+02 7 5.42 1209.90 5273.21 1208.09 0.3327E+02 0.5062E+03 0.3303E+02 8 6.83 1249.27 5840.64 1250.95 0.2785E+02 0.3242E+03 0.2760E+02 9 8.25 1288.64 6235.48 1286.60 0.2330E+02 0.2408E+03 0.2311E+02 10 9.41 1311.38 6489.21 1311.95 0.1956E+02 0.2004E+03 0.2066E+02 11 10.57 1334.12 6704.86 1335.02 0.1956E+02 0.1723E+03 0.1915E+02 12 11.74 1356.86 6892.59 1356.72 0.1862E+02 0.1517E+03 0.1827E+02 13 13.09 1380.62 7085.38 1381.05 0.1753E+02 0.1336E+03 0.1766E+02 14 14.45 1404.39 7256.61 1404.69 0.1753E+02 0.1196E+03 0.1722E+02 15 15.80 1428.15 7411.04 1427.75 0.1753E+02 0.1086E+03 0.1678E+02 16 17.16 1451.92 7551.98 1450.17 0.1614E+02 0.9960E+02 0.1629E+02 17 18.50 1471.77 7680.78 1471.72 0.1476E+02 0.9217E+02 0.1574E+02 18 19.85 1491.62 7800.38 1492.49 0.1476E+02 0.8589E+02 0.1515E+02 19 21.19 1511.46 7912.17 1512.45 0.1476E+02 0.8049E+02 0.1455E+02 20 22.54 1531.31 8017.18 1531.62 0.1476E+02 0.7580E+02 0.1397E+02 21 23.88 1551.16 8116.28 1550.03 0.1359E+02 0.7168E+02 0.1342E+02 22 25.27 1568.30 8212.86 1568.26 0.1238E+02 0.6794E+02 0.1292E+02 23 26.65 1585.43 8304.53 1585.82 0.1238E+02 0.6461E+02 0.1248E+02 24 28.03 1602.56 8391.85 1602.83 0.1238E+02 0.6162E+02 0.1210E+02 25 29.42 1619.70 8475.25 1619.34 0.1238E+02 0.5893E+02 0.1178E+02 --------------------------------------------------------------------------------------------------




A.5 – 18


: :

© 2011 J. Ross Publishing, Inc. 1

2.2500" 2.5000"

nc = 2 X

pc = pic=

------------------------------


End plate extended on tension side only.


1) 2)

End plate extended on tension side only. ct = 1.5000" pt = 3.5000" li = 11.0000" cc = 0.2500" pit= 2.5000" pi = 3.0000" gt = 4.0000" gi = 4.0000" gc = 4.0000" tp = 1.2500" nt = 2 X 2 ni = 2 X 3

Remark

England Fasteners: A325- -3/4"D 15/16" Oversize holes Material : -Fy = 35.27 ksi Fu = 64.62 ksi

Major parameters

A.N.Sherbourne (1961) TEST A1

Column : 8 x 8 UC 35 Beam : 15 x 5 RSJ 42 Plate thickness : 1 1/4"

Tested by Test Id.

V - 10

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 19


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 20


: :


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------


Two 7/8" bolts used on either side of tension flange. Four 1" bolts in compression. Material grade 50B ( BS968 ).


Remark

End plate extended on tension side only. ct = -" pt = 4.5000" li = cc = -" pit= -" pi = gt = -" gi = -" gc = tp = 1.0200" nt = 2 X 2 ni = 2 1

England Fasteners: 10.9- -7/8"D 1 1/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

J.R.Bailey (1970) TEST A1-L

Column : 8 x 8 UC 48 Beam : 12 x 5 RSJ 32 Plate thickness : 1"

Tested by Test Id.

V - 11

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

pic

pi pi

pit

pt

ct

24

30

36

42

48

Material : -: Experimental : M. Exponential


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 21


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1202E+03 -0.1344E+02 3 0.60 72.12 56.52 0.1202E+03 0.1603E+03 5 1.20 144.24 165.01 0.1838E+03 0.1905E+03 7 1.60 234.74 241.39 0.2263E+03 0.1905E+03 9 2.15 347.87 345.49 0.1939E+03 0.1884E+03 11 2.85 483.64 477.82 0.1940E+03 0.1907E+03 13 3.65 640.61 632.73 0.1980E+03 0.1966E+03 15 4.45 797.57 791.46 0.1939E+03 0.1993E+03 17 5.20 937.57 940.10 0.1803E+03 0.1960E+03 19 6.05 1094.54 1102.77 0.1886E+03 0.1856E+03 21 6.85 1238.79 1245.72 0.1697E+03 0.1711E+03 23 7.65 1361.82 1375.96 0.1414E+03 0.1542E+03 25 8.80 1527.28 1538.71 0.2014E+03 0.1289E+03 27 10.00 1705.45 1678.47 0.9757E+02 0.1045E+03 29 12.50 1883.64 1887.62 0.6390E+02 0.6561E+02 31 14.90 2010.91 2014.81 0.3679E+02 0.4226E+02 33 18.10 2112.73 2118.47 0.2683E+02 0.2437E+02 35 20.00 2155.15 2158.19 0.1993E+02 0.1781E+02 37 22.50 2193.33 2194.72 0.1414E+02 0.1182E+02 39 24.30 2214.55 2213.13 0.9433E+01 0.8775E+01 41 26.50 2231.52 2229.26 0.6302E+01 0.6049E+01 43 29.60 2240.00 2243.76 0.2341E+01 0.3519E+01 45 31.80 2248.49 2250.16 0.4446E+01 0.2364E+01 47 34.80 2265.46 2255.60 -0.1091E+02 0.1351E+01 ------------------------------------------------------------------------------



A.5 – 22

0.31025695E+05



: :


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------


Two 7/8" bolts used on either side of tension flange. Four 1" bolts in compression. Material grade 50B ( BS968 ).


Remark



Major parameters

J.R.Bailey (1970) TEST A1-R

Column : 8 x 8 UC 48 Beam : 12 x 5 RSJ 32 Plate thickness : 1"

Tested by Test Id.

V - 12

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 23


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.4000E+03 0.5512E+03 3 0.40 160.00 163.80 0.3509E+03 0.3118E+03 5 1.00 324.21 323.13 0.3158E+03 0.2522E+03 7 1.45 458.95 441.76 0.2863E+03 0.2780E+03 9 2.20 640.00 667.40 0.3744E+03 0.3181E+03 11 2.50 766.32 763.71 0.4391E+03 0.3228E+03 13 3.20 968.42 986.63 0.2731E+03 0.3091E+03 15 3.60 1086.31 1106.67 0.3053E+03 0.2901E+03 17 4.00 1212.64 1218.11 0.3263E+03 0.2665E+03 19 4.40 1347.37 1319.59 0.2877E+03 0.2406E+03 21 5.30 1524.22 1509.68 0.1804E+03 0.1826E+03 23 6.80 1726.32 1722.59 0.9992E+02 0.1069E+03 25 9.00 1877.89 1887.05 0.5264E+02 0.5191E+02 27 11.40 1970.53 1985.25 0.4001E+02 0.3394E+02 29 13.70 2063.16 2056.40 0.2959E+02 0.2852E+02 31 15.30 2105.27 2099.62 0.2616E+02 0.2546E+02 33 18.00 2172.64 2160.54 0.1804E+02 0.1953E+02 35 20.90 2206.32 2207.75 0.1298E+02 0.1317E+02 37 22.70 2231.58 2228.36 0.1090E+02 0.9832E+01 39 25.40 2248.42 2249.44 0.2966E+01 0.6024E+01 41 27.70 2256.84 2260.60 0.7353E+01 0.3819E+01 43 29.60 2265.26 2266.60 0.1110E-15 0.2566E+01 45 31.40 2265.26 2270.42 0.0000E+00 0.1736E+01 ------------------------------------------------------------------------------



A.5 – 24

0.58344139E+05



: :


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

V - 13


tp

column

------------------------------


Two 5/8" bolts used on either side of tension flange. Four 7/8" bolts in compression. Material grade 50B ( BS968 ).


Remark


England Fasteners: 10.9- -5/8"D 13/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters


Column : 8 x 8 UC 40 Beam : 10 x 4 UB 17 Plate thickness : 3/4"

Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

4

beam

12

16

20

24


8

cc

pc

pic

pi pi

pit

pt

ct

32


gt

li

36

40

nc

ni

nt

A.5 – 25


Moment ( kip-inch )

( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.8940E+02 0.2653E+02 3 0.20 17.88 10.74 0.8940E+02 0.7667E+02 5 0.40 35.75 29.42 0.8934E+02 0.1078E+03 7 0.60 53.63 53.20 0.8940E+02 0.1287E+03 9 1.10 116.74 126.47 0.1815E+03 0.1613E+03 11 1.60 207.48 212.47 0.1742E+03 0.1810E+03 13 2.00 275.23 286.82 0.2117E+03 0.1896E+03 15 2.40 376.86 363.29 0.2702E+03 0.1917E+03 17 2.70 461.56 420.53 0.2258E+03 0.1894E+03 19 3.30 529.30 530.86 0.1166E+03 0.1769E+03 21 4.00 613.99 647.06 0.1518E+03 0.1542E+03 23 4.40 681.74 705.88 0.1905E+03 0.1398E+03 25 4.80 766.43 758.92 0.1722E+03 0.1254E+03 27 5.40 834.18 828.03 0.1129E+03 0.1053E+03 29 6.00 901.93 885.80 0.9880E+02 0.8775E+02 31 7.30 986.62 980.14 0.8469E+02 0.5952E+02 33 8.90 1062.84 1057.42 0.3663E+02 0.3913E+02 35 11.00 1122.12 1123.13 0.1726E+02 0.2494E+02 37 13.10 1151.75 1166.07 0.1588E+02 0.1653E+02 39 14.65 1177.16 1188.07 0.1694E+02 0.1205E+02 41 16.10 1202.57 1203.08 0.1815E+02 0.8792E+01 43 17.55 1215.28 1213.93 0.0000E+00 0.6281E+01 45 19.15 1219.51 1222.25 0.4984E+01 0.4235E+01 47 20.75 1223.75 1227.80 0.0000E+00 0.2794E+01 49 22.50 1240.68 1231.70 0.7525E+01 0.1735E+01 51 24.10 1240.68 1233.93 0.2824E+01 0.1104E+01 53 26.10 1240.68 1235.61 -0.1059E+02 0.6158E+00 ------------------------------------------------------------------------------



A.5 – 26

0.25239341E+05



: :


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters



Tested by Test Id.

V - 14

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 27


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1364E+03 0.1273E+03 3 0.60 81.86 67.42 0.1364E+03 0.1328E+03 5 1.25 173.61 181.20 0.1452E+03 0.2117E+03 7 1.75 271.00 294.58 0.3105E+03 0.2356E+03 9 2.10 359.92 376.93 0.2117E+03 0.2327E+03 11 2.35 453.08 434.08 0.1016E+04 0.2237E+03 13 2.65 533.53 498.90 0.1186E+03 0.2077E+03 15 3.15 597.05 594.82 0.1355E+03 0.1753E+03 17 3.60 660.56 666.91 0.1482E+03 0.1454E+03 19 4.10 728.32 732.00 0.1270E+03 0.1158E+03 21 5.20 817.24 831.77 0.6091E+02 0.7023E+02 23 6.20 876.52 890.26 0.6275E+02 0.4934E+02 25 7.10 935.81 930.21 0.5960E+02 0.4051E+02 27 9.20 1020.49 1005.48 0.3296E+02 0.3231E+02 29 11.90 1088.24 1080.22 0.1431E+02 0.2254E+02 31 13.40 1105.18 1109.48 0.1129E+02 0.1651E+02 33 14.90 1122.12 1130.12 0.1193E+02 0.1117E+02 35 17.20 1143.29 1148.43 0.4236E+01 0.5224E+01 37 18.95 1147.52 1154.96 0.0000E+00 0.2460E+01 39 20.65 1151.76 1157.67 0.4459E+01 0.8803E+00 41 22.40 1156.00 1158.37 0.0000E+00 0.2168E-01 43 24.00 1160.23 1158.08 0.5287E+01 -0.3396E+00 45 25.65 1160.23 1157.39 -0.4976E+01 -0.4695E+00 47 27.55 1164.46 1156.48 0.8063E+01 -0.4634E+00 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.31333333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = 0.11219745E+04 -0.14679275E+05 0.53382787E+05 -0.87033319E+05 0.66038723E+05


A.5 – 28

-0.17677445E+05



: :


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters



Tested by Test Id.

V - 15

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 29


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.9774E+02 0.3842E+02 3 0.40 39.11 32.49 0.9777E+02 0.1108E+03 5 0.80 78.20 82.68 0.9777E+02 0.1363E+03 7 1.35 157.27 162.56 0.1700E+03 0.1529E+03 9 2.00 272.03 266.96 0.1842E+03 0.1677E+03 11 2.55 374.04 361.87 0.1870E+03 0.1766E+03 13 3.10 459.05 460.31 0.1275E+03 0.1804E+03 15 3.63 545.48 556.26 0.2064E+03 0.1786E+03 17 4.10 641.82 638.49 0.1870E+03 0.1732E+03 19 4.80 752.33 755.42 0.1568E+03 0.1600E+03 21 5.40 845.84 847.18 0.1426E+03 0.1455E+03 23 6.30 956.35 967.51 0.1425E+03 0.1217E+03 25 7.00 1066.87 1046.22 0.1295E+03 0.1033E+03 27 8.10 1160.38 1145.20 0.7146E+02 0.7735E+02 29 9.30 1228.39 1223.69 0.4564E+02 0.5445E+02 31 11.00 1279.39 1295.43 0.3318E+02 0.3169E+02 33 12.20 1321.90 1326.76 0.2723E+02 0.2116E+02 35 13.70 1347.40 1351.50 0.1372E+02 0.1253E+02 37 15.40 1364.40 1367.47 0.1032E+02 0.6804E+01 39 17.00 1381.40 1375.71 0.7084E+01 0.3784E+01 41 18.60 1387.07 1380.27 0.3540E+01 0.2088E+01 43 20.20 1385.65 1382.79 -0.5310E+01 0.1146E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.22500000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = -0.11957262E+03 0.73386630E+02 0.49286231E+04 -0.13983099E+05 0.61596652E+04


A.5 – 30

0.43268114E+04



: :


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters



Tested by Test Id.

V - 16

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 31


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2117E+03 0.2566E+03 3 0.47 98.80 100.86 0.2117E+03 0.1875E+03 5 1.00 199.01 194.99 0.1694E+03 0.1734E+03 7 1.60 300.64 303.37 0.1694E+03 0.1900E+03 9 2.15 402.27 412.62 0.2033E+03 0.2060E+03 11 2.55 503.90 496.31 0.3388E+03 0.2113E+03 13 2.95 597.05 580.84 0.1694E+03 0.2103E+03 15 3.20 639.40 633.01 0.5158E+00 0.2067E+03 17 3.80 732.55 752.70 0.1722E+03 0.1908E+03 19 4.30 825.71 843.67 0.2122E+03 0.1726E+03 21 4.70 918.86 909.50 0.1962E+03 0.1565E+03 23 5.30 1003.55 996.01 0.1396E+03 0.1320E+03 25 6.10 1113.65 1089.41 0.1173E+03 0.1022E+03 27 7.30 1181.40 1189.92 0.5594E-01 0.6745E+02 29 9.05 1270.32 1278.57 0.3257E+02 0.3734E+02 31 10.80 1333.84 1329.65 0.2658E+02 0.2279E+02 33 12.10 1359.24 1355.20 0.1539E+02 0.1698E+02 35 13.80 1376.18 1379.74 0.1067E+02 0.1225E+02 37 15.30 1393.12 1395.85 0.1571E+02 0.9363E+01 39 16.60 1418.52 1406.70 0.1341E+02 0.7387E+01 41 18.50 1426.99 1418.47 0.2229E+00 0.5115E+01 43 20.50 1418.52 1426.85 0.3441E+01 0.3361E+01 45 22.20 1435.46 1431.61 0.3223E+01 0.2292E+01 47 23.87 1429.82 1434.76 -0.3389E+01 0.1542E+01 ------------------------------------------------------------------------------



A.5 – 32

0.22819350E+05



: :


Major parameters pc =

2.7500"

------------------------------


7" x 3" shear plate welded to column to support end plate. Half length column web stiffner used in compression region.


1) 2)

End plate extended on tension side only. ct = 1.5000" pt = 4.5000" li = 7.0000" cc = 0.2500" gt = 3.5000" gc = 3.5000" tp = 0.7500" nt = 2 X 2 nc = 2 X 1

Remark

England

Fasteners: 10.9- -3/4"D 15/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

J.O.Surtees & A.P.Mann (1970) TEST C1


Tested by Test Id.

V - 17

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

2

6

8

cc

pc

pic

pi pi

pit

pt

ct

12

14

16


10

Material : : :


4

beam

gt

18

li

20

nc

ni

nt

A.5 – 33


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 34


: :



2.7500"

------------------------------




1) 2)


Remark

England

Fasteners: 10.9- -3/4"D 15/16" Oversize holes Material : -Fy = -ksi Fu = -ksi



Tested by Test Id.

V - 18

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

pic

pi pi

pit

pt

ct

36

42

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 35


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6006E+03 0.1938E+03 0.6287E+03 3 0.40 240.23 77.75 215.20 0.4902E+03 0.1954E+03 0.4675E+03 5 1.00 435.01 197.24 464.13 0.3884E+03 0.2043E+03 0.3837E+03 7 1.50 655.76 302.73 653.32 0.4277E+03 0.2190E+03 0.3783E+03 9 2.10 902.50 442.45 884.46 0.4004E+03 0.2495E+03 0.3934E+03 11 2.70 1136.23 605.82 1124.68 0.3896E+03 0.2978E+03 0.4057E+03 13 3.40 1408.93 830.97 1409.17 0.3779E+03 0.3289E+03 0.4040E+03 15 4.00 1629.68 1009.10 1647.34 0.3679E+03 0.2544E+03 0.3879E+03 17 4.60 1850.44 1137.17 1872.52 0.3787E+03 0.1780E+03 0.3612E+03 19 5.20 2084.17 1229.02 2079.45 0.3553E+03 0.1323E+03 0.3277E+03 21 5.90 2304.92 1309.77 2293.75 0.3028E+03 0.1012E+03 0.2842E+03 23 7.10 2616.58 1411.99 2589.57 0.2052E+03 0.7247E+02 0.2098E+03 25 9.00 2876.29 1526.48 2892.27 0.1124E+03 0.5074E+02 0.1148E+03 27 11.00 3058.09 1615.14 3054.22 0.5562E+02 0.3910E+02 0.5332E+02 29 13.40 3148.98 1698.44 3162.21 0.2965E+02 0.3100E+02 0.3026E+02 31 16.30 3226.90 1779.02 3226.08 0.3508E+02 0.2505E+02 0.1697E+02 33 18.80 3278.84 1837.11 3264.97 0.1011E+02 0.2162E+02 0.1480E+02 35 21.40 3304.81 1889.75 3303.16 0.1730E+02 0.1900E+02 0.1469E+02 37 23.80 3343.76 1933.04 3338.45 0.1097E+02 0.1714E+02 0.1468E+02 39 26.20 3369.74 1972.32 3373.41 0.1998E+02 0.1565E+02 0.1442E+02 41 28.50 3395.71 2007.16 3406.11 -0.3710E+01 0.1446E+02 0.1400E+02 43 31.50 3434.66 2048.33 3447.19 0.1232E+02 0.1319E+02 0.1340E+02 45 34.40 3473.63 2085.07 3485.28 0.2139E+02 0.1218E+02 0.1289E+02 47 37.00 3525.56 2115.71 3518.32 0.1600E+02 0.1141E+02 0.1254E+02 49 39.90 3564.52 2147.83 3554.26 0.1180E+02 0.1066E+02 0.1226E+02 --------------------------------------------------------------------------------------------------




A.5 – 36


: :



2.7500"

V - 19


tp

column

------------------------------




1) 2)


Remark

England

Fasteners: 10.9- -1"D 1 1/4" Oversize holes Material : -Fy = -ksi Fu = -ksi



Tested by Test Id.


0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

0

6

beam

18

24

30

36

42

48


cc

pc

pic

pi pi

pit

pt

ct


12

Material : : :

gt

li

54

60

nc

ni

nt

A.5 – 37


Moment ( kip-inch )

R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6709E+03 0.2984E+03 0.7484E+03 3 0.30 201.28 89.58 238.59 0.8765E+03 0.2998E+03 0.8285E+03 5 0.60 525.91 180.00 490.62 0.9523E+03 0.3040E+03 0.8434E+03 7 0.90 772.63 272.39 740.80 0.7343E+03 0.3113E+03 0.8197E+03 9 1.30 1019.36 399.74 1056.84 0.6848E+03 0.3266E+03 0.7565E+03 11 1.60 1240.12 500.11 1275.26 0.7544E+03 0.3433E+03 0.6988E+03 13 2.00 1551.77 643.28 1538.83 0.7142E+03 0.3744E+03 0.6192E+03 15 2.40 1811.47 801.35 1771.09 0.5569E+03 0.4181E+03 0.5431E+03 17 2.90 2032.24 1027.14 2020.85 0.4179E+03 0.4852E+03 0.4580E+03 19 3.50 2265.97 1330.54 2269.20 0.3548E+03 0.4956E+03 0.3728E+03 21 4.30 2512.69 1661.29 2530.65 0.3053E+03 0.3262E+03 0.2854E+03 23 4.90 2694.49 1826.73 2686.38 0.2705E+03 0.2342E+03 0.2357E+03 25 6.25 2941.22 2068.11 2947.86 0.2020E+03 0.1395E+03 0.1582E+03 27 7.60 3148.98 2226.79 3126.49 0.1094E+03 0.1000E+03 0.1099E+03 29 9.90 3330.78 2415.98 3317.18 0.6141E+02 0.6878E+02 0.6076E+02 31 12.20 3408.70 2554.50 3421.51 0.2597E+02 0.5317E+02 0.3240E+02 33 14.30 3460.64 2656.32 3471.74 0.1771E+02 0.4440E+02 0.1672E+02 35 16.60 3486.61 2750.44 3497.53 0.2001E+02 0.3783E+02 0.6714E+01 37 18.80 3525.56 2828.42 3506.13 -0.3629E+01 0.3328E+02 0.1670E+01 39 21.90 3512.58 2923.93 3505.94 -0.9742E-13 0.2860E+02 -0.1201E+01 41 24.50 3486.61 2994.33 3501.91 -0.1036E+02 0.2567E+02 -0.1726E+01 43 27.50 3512.58 3067.20 3496.92 0.7276E+01 0.2302E+02 -0.1529E+01 45 29.90 3486.61 3120.75 3493.64 -0.1085E+02 0.2129E+02 -0.1195E+01 47 32.60 3499.60 3176.13 3490.91 -0.1374E+01 0.1967E+02 -0.8335E+00 49 34.70 3486.61 3216.05 3489.41 -0.3905E+01 0.1860E+02 -0.6050E+00 51 38.40 3473.63 3281.52 3487.74 -0.3124E+01 0.1699E+02 -0.3246E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.37083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = -0.56948661E+03 -0.16720282E+04 0.19191749E+05 -0.47007293E+05 0.51737667E+05



A.5 – 38


: :



2.7500"

------------------------------




1) 2)


Remark

England



Column : 10 x 10 UC 60 Beam : 15 x 6 UB 40 Plate thickness : 1"

Tested by Test Id.

V - 20

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

pic

pi pi

pit

pt

ct

36

42

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 39


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3159E+03 0.3348E+03 0.5462E+02 3 0.80 252.73 270.84 245.52 0.3299E+03 0.3461E+03 0.4090E+03 5 1.70 563.78 599.98 587.88 0.3387E+03 0.3927E+03 0.3383E+03 7 2.40 797.06 899.07 808.51 0.3441E+03 0.4691E+03 0.3009E+03 9 3.20 1082.20 1320.84 1051.72 0.3446E+03 0.5732E+03 0.3147E+03 11 4.10 1380.29 1786.13 1354.04 0.3324E+03 0.4134E+03 0.3578E+03 13 4.80 1613.58 2022.63 1614.38 0.3441E+03 0.2763E+03 0.3835E+03 15 5.60 1898.71 2207.21 1925.86 0.3737E+03 0.1944E+03 0.3909E+03 17 6.30 2170.87 2328.07 2195.76 0.3737E+03 0.1542E+03 0.3773E+03 19 7.10 2456.00 2438.98 2485.12 0.3873E+03 0.1252E+03 0.3434E+03 21 7.70 2702.26 2509.33 2681.26 0.3499E+03 0.1100E+03 0.3095E+03 23 8.60 2935.55 2600.44 2916.15 0.2500E+03 0.9343E+02 0.2118E+03 25 10.00 3194.75 2718.27 3150.54 0.1206E+03 0.7617E+02 0.1248E+03 27 13.10 3350.28 2917.61 3391.56 0.2710E+02 0.5494E+02 0.4170E+02 29 15.60 3415.08 3042.02 3443.94 0.2097E+02 0.4533E+02 0.7685E+01 31 17.90 3452.84 3138.91 3454.42 0.1654E+02 0.3925E+02 0.4058E+01 33 20.30 3492.84 3227.24 3470.21 0.1412E+02 0.3458E+02 0.9685E+01 35 22.50 3518.76 3299.52 3497.85 0.1353E+02 0.3126E+02 0.1516E+02 37 26.40 3583.57 3412.31 3567.07 0.9651E+01 0.2684E+02 0.1901E+02 39 28.90 3596.53 3477.25 3613.76 0.1129E+02 0.2464E+02 0.1802E+02 41 31.20 3635.41 3531.81 3652.88 0.1575E+02 0.2297E+02 0.1588E+02 43 33.90 3674.29 3591.63 3691.73 0.1608E+02 0.2130E+02 0.1288E+02 45 36.80 3726.13 3651.17 3724.56 0.1708E+02 0.1979E+02 0.9835E+01 47 40.00 3777.97 3712.22 3751.49 0.1620E+02 0.1837E+02 0.7122E+01 --------------------------------------------------------------------------------------------------




A.5 – 40


: :



2.7500"

------------------------------




1) 2)


Remark

England



Column : 10 x 10 UC 60 Beam : 15 x 6 UB 40 Plate thickness : 1"

Tested by Test Id.

V - 21

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

pic

pi pi

pit

pt

ct

36

42

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 41


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 42


: :



1.9685"

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 42.80 0.50 3 83.30 1.00 4 122.00 1.50 5 158.70 2.00 6 190.20 2.50 7 221.20 3.00 8 276.50 3.50 9 335.70 4.00 10 369.50 5.00 11 411.10 6.00 12 458.00 8.00 13 494.40 10.00 14 528.20 12.40 15 562.10 15.00 16 614.10 20.00 17 658.30 25.10 18 687.00 29.90 19 713.00 35.10 20 736.40 39.80 21 759.80 45.00 22 778.00 50.10 23 801.50 55.00 24 817.10 60.00 25 832.70 65.00 -----------------------------------------------------------


1) End plate extended on tension side only. Tension side hole is 0.811" D. 2) Hsfg bolts used on the side of tension flange. Comp.side hole is 0.689" D.


Remark

England


J.A.Packer & L.J.Morris (1977) TEST J1

Column : 152 x 152 UC 37 Beam : 254 x 102 UB 22 Plate thickness : 15 mm

Tested by Test Id.

V - 22

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

17

51

68

cc

pc

pic

pi pi

pit

pt

ct

li

nc

ni

nt

102 119 136 153 170


85

Material : : :


34

beam

gt

A.5 – 43


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.8560E+02 0.5250E+02 0.5637E+02 3 1.00 83.30 53.42 74.32 0.7920E+02 0.5532E+02 0.8549E+02 5 2.00 158.70 113.16 161.64 0.6820E+02 0.6587E+02 0.8614E+02 7 3.00 221.20 189.32 242.78 0.8630E+02 0.8738E+02 0.7509E+02 9 4.00 335.70 273.37 310.82 0.9020E+02 0.6887E+02 0.6088E+02 11 6.00 411.10 357.43 406.54 0.3555E+02 0.2652E+02 0.3637E+02 13 10.00 494.40 426.21 498.96 0.1633E+02 0.1194E+02 0.1495E+02 15 15.00 562.10 472.65 560.06 0.1214E+02 0.7411E+01 0.1096E+02 17 25.10 658.30 529.47 655.17 0.7282E+01 0.4412E+01 0.7539E+01 19 35.10 713.00 567.02 716.12 0.4989E+01 0.3239E+01 0.5075E+01 21 45.00 759.80 595.65 761.49 0.4030E+01 0.2599E+01 0.4173E+01 23 55.00 801.50 619.43 798.97 0.3966E+01 0.2185E+01 0.3286E+01 25 65.00 832.70 639.75 826.81 0.2600E+01 0.1895E+01 0.2284E+01 27 75.00 848.30 657.57 845.15 0.7800E+00 0.1679E+01 0.1423E+01 29 85.00 853.50 673.49 856.13 0.2600E+00 0.1512E+01 0.8171E+00 31 95.20 853.50 688.20 862.35 -0.2394E+01 0.1376E+01 0.4363E+00 33 104.90 791.00 701.10 785.03 -0.1198E+02 0.1270E+01 -0.8064E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10191667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.10564292E+04 0.10048125E+05 -0.38583394E+05 0.78494463E+05 -0.78286630E+05 Rj0 = 95.2000 RKj = -0.82945744E+01



A.5 – 44


: :



1.9685"



1) End plate extended on tension side only. Tension side hole is 0.811" D. 2) Hsfg bolts used on the side of tension flange. Comp.side hole is 0.689" D.


Remark

England




Tested by Test Id.

V - 23

0

95

190

285

380

475

570

665

760

855

950

tp

column

Moment ( kip-inch )


0

18

54

72

cc

pc

pic

pi pi

pit

pt

ct

li

nc

ni

nt

108 126 144 162 180


90

Material : : :


36

beam

gt

A.5 – 45


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6800E+02 0.5250E+02 0.5251E+02 3 1.00 65.10 53.42 69.73 0.6500E+02 0.5532E+02 0.7998E+02 5 2.00 137.90 113.16 150.41 0.8100E+02 0.6587E+02 0.7832E+02 7 3.00 252.40 189.32 222.59 0.1113E+03 0.8738E+02 0.6506E+02 9 6.00 338.30 357.44 350.65 0.1888E+02 0.2652E+02 0.2381E+02 11 10.00 395.50 426.21 401.11 0.1170E+02 0.1194E+02 0.7439E+01 13 14.00 442.40 464.93 434.03 0.1064E+02 0.7994E+01 0.9782E+01 15 18.10 481.40 493.39 478.88 0.9269E+01 0.6085E+01 0.1146E+02 17 25.00 541.20 529.02 547.89 0.7386E+01 0.4429E+01 0.7810E+01 19 35.00 595.90 566.69 597.56 0.4382E+01 0.3247E+01 0.3088E+01 21 45.10 632.30 595.91 625.86 0.2860E+01 0.2594E+01 0.2923E+01 23 55.10 658.30 619.65 657.95 0.2895E+01 0.2181E+01 0.3395E+01 25 65.00 687.00 639.75 690.73 0.2610E+01 0.1895E+01 0.3107E+01 27 75.00 713.00 657.57 718.17 0.2600E+01 0.1679E+01 0.2348E+01 29 85.20 739.00 673.79 737.95 0.2045E+01 0.1509E+01 0.1550E+01 31 95.20 757.20 688.20 750.25 0.7153E+00 0.1376E+01 0.9458E+00 33 105.10 757.20 701.40 757.49 0.2352E+00 0.1267E+01 0.5470E+00 35 112.90 733.80 710.94 729.47 -0.7582E+01 0.1195E+01 -0.7717E+01 --------------------------------------------------------------------------------------------------




A.5 – 46


: :



1.9685"



1) End plate extended on tension side only. Tension side hole is 0.811" D. 2) Hsfg bolts used on the side of tension flange. Comp.side hloe is 0.689" D.


Remark

England




Tested by Test Id.

V - 24

0

85

170

255

340

425

510

595

680

765

850

tp

column

Moment ( kip-inch )


0

20

60

80


cc

pc

pic

pi pi

pit

pt

ct

li

nc

ni

nt

100 120 140 160 180 200

Material : : :


40

beam

gt

A.5 – 47


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7000E+02 0.5250E+02 0.6526E+02 3 1.00 65.10 53.42 59.99 0.5542E+02 0.5532E+02 0.5497E+02 5 3.00 150.00 189.22 152.98 0.3848E+02 0.8736E+02 0.3899E+02 7 5.10 221.20 329.23 222.24 0.2972E+02 0.3746E+02 0.2780E+02 9 7.00 268.00 380.50 268.43 0.1950E+02 0.2008E+02 0.2129E+02 11 9.00 307.10 413.42 306.32 0.1825E+02 0.1374E+02 0.1695E+02 13 12.00 353.90 447.52 351.10 0.1430E+02 0.9533E+01 0.1332E+02 15 16.00 400.70 479.78 399.16 0.9750E+01 0.6918E+01 0.1098E+02 17 20.00 439.80 504.38 440.02 0.9041E+01 0.5502E+01 0.9499E+01 19 25.10 478.80 529.43 483.94 0.8347E+01 0.4413E+01 0.7710E+01 21 29.90 517.80 548.92 516.78 0.7114E+01 0.3748E+01 0.5972E+01 23 40.00 564.70 581.97 560.12 0.2610E+01 0.2883E+01 0.2787E+01 25 50.20 585.50 608.53 585.49 0.1523E+01 0.2363E+01 0.2374E+01 27 60.00 598.50 629.95 603.94 0.1820E+01 0.2028E+01 0.1521E+01 29 70.10 614.10 649.10 617.55 0.1611E+01 0.1777E+01 0.1244E+01 31 80.20 629.70 666.05 629.94 0.1341E+01 0.1588E+01 0.1233E+01 33 90.20 645.30 681.16 642.60 0.1258E+01 0.1439E+01 0.1305E+01 35 100.10 658.30 694.80 655.91 0.1300E+01 0.1320E+01 0.1382E+01 37 110.00 671.30 707.37 669.90 0.1571E+01 0.1221E+01 0.1442E+01 39 120.10 684.40 719.27 684.70 0.7800E+00 0.1136E+01 0.1484E+01 41 128.90 684.40 728.98 683.59 -0.2325E+01 0.1072E+01 -0.2250E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12133333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.29381606E+02 0.13838610E+03 0.45781317E+04 -0.16771691E+05 0.20302012E+05 Rj0 = 45.0000 125.1000 RKj = 0.15443870E+01 -0.37571595E+01



A.5 – 48


: :

© 2011 J. Ross Publishing, Inc. pc = gc =

1.8750" 6.0000"

------------------------------


End plate extended on tension side only. Hs bolts used.


1) 2)

End plate extended on tension side only. ct = 1.5000" pt = 3.7500" li = 20.1594" cc = 2.7156" gt = 3.5000" gt2= 2.5000" tp = 1.0000" nt = 4 X 2 nc = 2 X 1

Remark

Australia Fasteners: 10.9- -7/8"D 1 1/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

P.Grundy et al. (1980) T1

Column : 310 UC 240 Beam : 610 UB 113 Plate thickness : 1"

Tested by Test Id.

V - 25

0 0.0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

tp

column

Moment ( kip-inch )


0.7

2.1

2.8

cc

pc

pic

pi pi

pit

pt

ct

4.2

4.9

5.6


3.5

Material : : :


1.4

beam

gt

6.3

li

7.0

nc

ni

nt

A.5 – 49


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.64166667E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.18874873E+04 0.40768165E+05 -0.25342062E+06 0.67233791E+06 -0.80586571E+06 Rj0 = 4.0000 4.4000 RKj = -0.37328426E+03 0.80642140E+03



A.5 – 50


: :

© 2011 J. Ross Publishing, Inc. pc = gc =

1.8750" 6.0000"

------------------------------


End plate extended on tension side only. Hs bolts used.


1) 2)

End plate extended on tension side only. ct = 1.5000" pt = 3.7500" li = 20.1594" cc = 2.7156" gt = 3.5000" gt2= 2.5000" tp = 1.2500" nt = 4 X 2 nc = 2 X 1

Remark

Australia Fasteners: 10.9- -7/8"D 1 1/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

P.Grundy et al. (1980) T2

Column : 310 UC 240 Beam : 610 UB 113 Plate thickness : 1 1/4"

Tested by Test Id.

V - 26

0 0.0

1050

2100

3150

4200

5250

6300

7350

8400

9450

10500

tp

column

Moment ( kip-inch )


0.8

2.4

3.2

cc

pc

pic

pi pi

pit

pt

ct

4.8

5.6

6.4


4.0

Material : : :


1.6

beam

gt

7.2

li

8.0

nc

ni

nt

A.5 – 51


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3082E+04 0.9952E+03 0.1315E+04 3 0.20 616.44 199.08 635.00 0.3082E+04 0.9972E+03 0.3439E+04 5 0.40 1232.88 398.77 1242.02 0.3149E+04 0.1003E+04 0.2790E+04 7 0.67 2095.89 668.01 2039.31 0.3236E+04 0.1018E+04 0.3344E+04 9 0.90 2835.61 907.83 2891.26 0.3082E+04 0.1038E+04 0.3883E+04 11 1.05 3452.05 1065.19 3481.06 0.6164E+04 0.1055E+04 0.3941E+04 13 1.20 4099.31 1223.98 4062.88 0.3390E+04 0.1074E+04 0.3786E+04 15 1.40 4777.40 1441.87 4780.79 0.3390E+04 0.1106E+04 0.3364E+04 17 1.60 5393.84 1666.62 5401.88 0.2774E+04 0.1145E+04 0.2841E+04 19 1.80 5948.63 1899.93 5918.20 0.2774E+04 0.1192E+04 0.2330E+04 21 2.10 6503.43 2271.48 6517.95 0.1387E+04 0.1281E+04 0.1701E+04 23 2.55 7058.22 2886.10 7136.64 0.1110E+04 0.1460E+04 0.1113E+04 25 3.00 7551.37 3588.81 7562.84 0.1079E+04 0.1656E+04 0.8144E+03 27 3.40 7890.41 4266.35 7856.04 0.6164E+03 0.1689E+04 0.6619E+03 29 3.85 8136.98 4975.57 8124.59 0.4932E+03 0.1424E+04 0.5361E+03 31 4.25 8321.92 5483.33 8319.36 0.4110E+03 0.1122E+04 0.4393E+03 33 4.55 8445.20 5791.46 8441.02 0.4110E+03 0.9400E+03 0.3726E+03 35 4.95 8568.49 6129.77 8573.63 0.2466E+03 0.7621E+03 0.2923E+03 37 5.35 8660.96 6411.42 8676.37 0.2055E+03 0.6360E+03 0.2234E+03 39 5.70 8660.96 6616.54 8669.59 -0.1541E+03 0.5569E+03 -0.2064E+03 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.74166667E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.67783540E+04 0.99580227E+05 -0.44904916E+06 0.89263576E+06 -0.85158317E+06 Rj0 = 5.5000 RKj = -0.37967754E+03



A.5 – 52


: :



V - 27

tp

column

------------------------------


2.2500" 2.5000"

nc = 2 X

pc = pic=




1) 2)


Remark


Major parameters

Column : 8 x 8 UC 35 Beam : 15 x 5 RSJ 42 Plate thickness : 1 1/4" Stiffener thickness : 0.3125"

Tested by Test Id.

Connection type : Extended end-plate connections Mode : All bolted with column stiffener

0

650

1300

1950

2600

3250

3900

4550

5200

5850

6500

0

4

beam

12

16

20

24


8

cc

pc

pic

pi pi

pit

pt

ct

32


gt

li

36

40

nc

ni

nt

A.5 – 53


Moment ( kip-inch )

A3 = P3 =

2.040000 5

K = Q1 =

0.001427 0 Q2 =

R = Sum ( Ai X ( K*Bm )**Pi X 10**Qi )

( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4046E+04 0.3914E+03 0.5528E+04 3 0.10 404.61 39.13 476.53 0.4046E+04 0.3910E+03 0.4084E+04 5 0.20 809.22 78.21 830.81 0.1380E+06 0.3899E+03 0.3062E+04 7 0.20 1090.68 78.21 830.81 0.1399E+06 0.3899E+03 0.3062E+04 9 0.53 1442.51 206.76 1525.59 0.1056E+04 0.3800E+03 0.1446E+04 11 0.80 1776.76 306.07 1853.22 0.1583E+04 0.3634E+03 0.1082E+04 13 1.10 2075.81 411.03 2156.88 0.7036E+03 0.3348E+03 0.9654E+03 15 1.30 2462.83 475.68 2345.94 0.2439E+06 0.3113E+03 0.9257E+03 17 1.50 2744.29 535.45 2526.81 0.1275E+04 0.2863E+03 0.8812E+03 19 2.40 3131.31 746.37 3187.38 0.7037E+03 0.1891E+03 0.5690E+03 21 2.95 3412.78 839.20 3449.07 0.4021E+03 0.1507E+03 0.3919E+03 23 3.80 3729.42 949.81 3707.38 0.2890E+03 0.1129E+03 0.2395E+03 25 5.30 4046.08 1089.39 4007.88 0.1847E+03 0.7756E+02 0.1832E+03 27 7.00 4327.54 1202.33 4297.27 0.1477E+03 0.5744E+02 0.1502E+03 29 9.20 4538.64 1311.62 4536.50 0.1077E+03 0.4331E+02 0.6597E+02 31 10.70 4679.38 1371.77 4690.22 0.8377E+02 0.3724E+02 0.8127E+02 33 12.70 4820.10 1440.16 4816.85 0.5470E+02 0.3150E+02 0.5058E+02 35 14.40 4890.47 1490.54 4895.14 0.4861E+02 0.2793E+02 0.4355E+02 37 15.70 4960.84 1525.37 4951.74 0.5227E+02 0.2573E+02 0.4406E+02 39 17.10 5031.20 1559.98 5015.25 0.4865E+02 0.2376E+02 0.4687E+02 41 18.60 5101.57 1594.23 5088.26 0.4432E+02 0.2197E+02 0.5046E+02 43 20.30 5171.94 1630.10 5177.18 -0.1274E+02 0.2027E+02 0.5400E+02 45 20.95 5207.12 1643.43 5212.64 0.4139E+02 0.1968E+02 0.5511E+02 47 21.60 5242.31 1655.73 5248.79 0.8704E-12 0.1916E+02 0.5607E+02 49 23.10 5242.31 1683.58 5247.73 0.1454E-12 0.1802E+02 -0.8764E+01 51 24.40 5242.31 1706.72 5237.06 0.0000E+00 0.1714E+02 -0.7719E+01 --------------------------------------------------------------------------------------------------


Frye and Morris polynominal model : xd = 14.500000" t = 1.250000" A1 = 1.790000 A2 = 1.760000 P1 = 1 P2 = 3


A.5 – 54


: :



2.2500" 2.5000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters

Column : 8 x 8 UC 35 Beam : 15 x 5 RSJ 42 Plate thickness : 3/4" Stiffener thickness : 0.6250"

Tested by Test Id.

V - 28

0

750

1500

2250

3000

3750

4500

5250

6000

6750

7500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 55


A3 = P3 =

2.040000 5

K = Q1 =

0.001939 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 56


: :

A.N.Sherbourne (1961) TEST B1


V - 29

tp

column

------------------------------


3.5000" 3.0000"

nc = 2 X

pc = pic=




1) 2)


Remark

England Fasteners: A325- -7/8"D 1 1/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

Column : 8 x 8 UC 35 Beam : 15 x 5 RSJ 42 Plate thickness : 1" Stiffener thickness : 0.3125"

Tested by Test Id.


0

700

1400

2100

2800

3500

4200

4900

5600

6300

7000

0

10

beam

30

40

50

60

70

80


cc

pc

pic

pi pi

pit

pt

ct


20

Material : : :

gt

li

90

100

nc

ni

nt

A.5 – 57


Moment ( kip-inch )

A3 = P3 =

2.040000 5

K = Q1 =

0.001775 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2639E+04 0.3147E+03 0.2677E+04 3 0.20 527.75 62.90 487.03 0.2193E+04 0.3135E+03 0.2209E+04 5 0.50 985.13 156.05 1062.94 0.1665E+04 0.3067E+03 0.1657E+04 7 0.70 1336.97 216.58 1442.65 0.1671E+04 0.2980E+03 0.1760E+04 9 0.90 1653.61 274.98 1770.23 0.2873E+04 0.2854E+03 0.1524E+04 11 1.00 2005.44 303.33 1917.47 0.2873E+04 0.2776E+03 0.1423E+04 13 1.20 2322.10 356.95 2183.90 0.1495E+04 0.2600E+03 0.1248E+04 15 1.40 2603.56 407.00 2418.66 0.1255E+04 0.2403E+03 0.1105E+04 17 2.20 2990.58 568.31 3142.41 0.4496E+03 0.1664E+03 0.7526E+03 19 3.60 3377.59 745.26 3395.05 0.1759E+03 0.9644E+02 0.1034E+03 21 5.45 3660.26 885.23 3650.38 0.1352E+03 0.6046E+02 0.1205E+03 23 7.70 3909.24 997.50 3899.11 0.9007E+02 0.4179E+02 0.1010E+03 25 10.70 4156.18 1102.97 4162.02 0.7501E+02 0.2994E+02 0.7465E+02 27 13.40 4326.30 1175.23 4337.79 0.4938E+02 0.2405E+02 0.5688E+02 29 17.70 4538.64 1265.60 4546.46 0.4435E+02 0.1849E+02 0.4233E+02 31 21.10 4679.38 1323.48 4679.96 0.2433E-01 0.1574E+02 0.3660E+02 33 23.60 4784.92 1360.85 4767.24 0.3927E+02 0.1421E+02 0.3328E+02 35 27.40 4887.76 1411.31 4884.65 0.2221E+02 0.1243E+02 0.2855E+02 37 30.80 4966.25 1451.41 4974.84 0.1861E+02 0.1121E+02 0.2457E+02 39 35.30 5101.57 1498.86 5074.87 0.1486E+02 0.9938E+01 0.2006E+02 41 38.90 5136.76 1533.41 5141.85 0.2199E+02 0.9124E+01 0.1727E+02 43 42.10 5189.53 1561.59 5193.98 0.1100E+02 0.8520E+01 0.1539E+02 45 46.50 5277.49 1597.28 5257.43 0.1279E+02 0.7823E+01 0.1358E+02 47 51.70 5312.68 1636.46 5324.41 0.1375E+02 0.7137E+01 0.1230E+02 49 57.70 5418.22 1676.99 5395.63 0.1153E+02 0.6503E+01 0.1153E+02 51 61.60 5453.40 1701.70 5440.04 0.3518E+02 0.6150E+01 0.1127E+02 --------------------------------------------------------------------------------------------------




A.5 – 58


: :

A.N.Sherbourne (1961) TEST B2


3.5000" 3.0000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark

England Fasteners: A325- -7/8"D 1 1/16" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

Column : 8 x 8 UC 35 Beam : 15 x 5 RSJ 42 Plate thickness : 3/4" Stiffener thickness : 0.5000"

Tested by Test Id.

V - 30

0

650

1300

1950

2600

3250

3900

4550

5200

5850

6500

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

pic

pi pi

pit

pt

ct

36

42

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 59


A3 = P3 =

2.040000 5

K = Q1 =

0.002110 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 60


: :


Major parameters

1

2.0000" 3.0000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark

England


L.G.Johnson et al. (1960) TEST 5

Column : 8 x 8 UC 45 Beam : 10 x 4 1/2 RSJ 2 Plate thickness : 1/2" Stiffener thickness : 0.5000"

Tested by Test Id.

V - 31

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

3

9

12

cc

pc

pic

pi pi

pit

pt

ct

18

21

24


15

Material : : :


6

beam

gt

27

li

30

nc

ni

nt

A.5 – 61


A3 = P3 =

2.040000 5

K = Q1 =

0.006412 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 62


: :

J.R.Bailey (1970) B4-L


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------


End plate extended on tension side only. Material grade 43A ( BS15 )


Remark



Major parameters

Column : 8 x 8 UC 40 Beam : 12 x 5 UB 32 Plate thickness : 1 1/4" Stiffener thickness : 0.3125"

Tested by Test Id.

V - 32

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 63


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2795E+03 0.5060E+03 3 0.50 139.74 190.11 -0.1863E+03 0.3034E+03 5 0.60 211.72 219.78 0.3599E+03 0.2910E+03 7 1.00 372.63 333.13 0.4446E+03 0.2845E+03 9 1.50 525.07 482.15 0.2117E+03 0.3135E+03 11 2.10 652.10 679.47 0.2117E+03 0.3399E+03 13 2.50 779.14 816.13 0.6352E+03 0.3411E+03 15 2.90 923.10 950.67 0.2682E+03 0.3297E+03 17 3.30 1071.30 1078.57 0.6775E+03 0.3085E+03 19 3.70 1219.51 1196.65 0.2682E+03 0.2811E+03 21 4.20 1410.06 1327.66 0.4497E+03 0.2425E+03 23 5.50 1587.90 1578.72 0.1486E+03 0.1472E+03 25 7.70 1757.28 1785.25 0.5909E+02 0.5587E+02 27 10.80 1918.19 1902.27 0.4740E+02 0.3045E+02 29 14.80 2045.22 2024.71 0.2358E+02 0.3010E+02 31 18.80 2129.90 2130.64 0.1647E+02 0.2187E+02 33 22.30 2180.72 2191.78 0.1390E+02 0.1332E+02 35 25.80 2214.59 2226.80 0.8511E+01 0.7156E+01 37 29.70 2256.94 2246.21 0.9579E+01 0.3238E+01 39 32.70 2282.34 2269.54 0.7783E+01 0.7069E+01 41 36.30 2299.28 2293.06 0.4640E+01 0.6116E+01 43 40.30 2316.22 2316.47 0.2167E+01 0.5663E+01 ------------------------------------------------------------------------------



A.5 – 64

-0.60053143E+04



: :

J.R.Bailey (1970) B4-R


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 33

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

8

24

cc

pc

pic

pi pi

pit

pt

ct

32

40

48

56

64



16

beam

gt

72

li

80

nc

ni

nt

A.5 – 65


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.3522E+03 0.2377E+03 3 0.60 211.32 227.60 0.1210E+04 0.4673E+03 5 0.70 346.57 274.99 0.1175E+04 0.4797E+03 7 1.20 490.26 518.76 0.4424E+03 0.4820E+03 9 1.50 650.87 659.64 0.4790E+03 0.4549E+03 11 1.80 777.66 790.79 0.3656E+03 0.4184E+03 13 2.30 912.90 983.14 0.1031E+04 0.3507E+03 15 2.40 1031.24 1017.54 0.1019E+04 0.3373E+03 17 2.80 1174.94 1142.14 0.3311E+03 0.2865E+03 19 3.50 1386.26 1315.47 0.2630E+03 0.2122E+03 21 5.20 1546.87 1573.98 0.8187E+02 0.1072E+03 23 7.70 1741.28 1761.79 0.7143E+02 0.5393E+02 25 10.40 1876.52 1877.38 0.4050E+02 0.3447E+02 27 13.20 1969.51 1959.38 0.2174E+02 0.2522E+02 29 16.20 2028.68 2027.20 0.1723E+02 0.2057E+02 31 19.80 2096.30 2095.43 0.1589E+02 0.1751E+02 33 23.60 2147.02 2156.25 0.1542E+02 0.1443E+02 35 27.50 2197.74 2205.81 0.9860E+01 0.1097E+02 37 31.50 2240.00 2242.83 0.7458E+01 0.7630E+01 39 35.30 2265.36 2266.76 0.6348E+01 0.5078E+01 41 39.00 2282.27 2281.99 0.2061E+01 0.3262E+01 43 42.70 2290.72 2291.61 0.5205E+01 0.2022E+01 45 45.70 2307.62 2296.59 0.3076E+01 0.1343E+01 47 48.80 2307.62 2299.97 0.0000E+00 0.8663E+00 ------------------------------------------------------------------------------



A.5 – 66

0.46358011E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters

Column : 8 x 8 UC 40 Beam : 14 x 5 UB 26 Plate thickness : 1" Stiffener thickness : 0.3125"

Tested by Test Id.

V - 34

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 67


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2182E+03 0.2063E+03 3 0.70 152.72 160.88 0.2790E+03 0.2568E+03 5 1.20 313.94 297.79 0.2970E+03 0.2884E+03 7 1.70 449.70 446.36 0.2767E+03 0.3029E+03 9 2.30 619.39 627.83 0.2616E+03 0.2985E+03 11 2.90 763.63 801.06 0.3125E+03 0.2768E+03 13 3.30 907.88 907.84 0.3295E+03 0.2566E+03 15 3.90 1077.58 1051.73 0.2475E+03 0.2226E+03 17 4.50 1204.85 1174.94 0.1814E+03 0.1883E+03 19 5.20 1306.67 1293.68 0.1293E+03 0.1518E+03 21 6.60 1442.42 1464.53 0.9044E+02 0.9644E+02 23 7.80 1544.24 1561.30 0.7839E+02 0.6731E+02 25 10.80 1713.94 1708.78 0.4965E+02 0.3785E+02 27 13.80 1824.24 1807.22 0.2334E+02 0.2872E+02 29 17.60 1892.12 1898.60 0.1658E+02 0.1934E+02 31 20.85 1943.03 1949.05 0.1357E+02 0.1197E+02 33 24.10 1976.96 1978.55 0.5502E+01 0.6547E+01 35 26.30 1985.46 1990.07 0.4083E+01 0.4072E+01 37 30.10 1993.94 2000.17 -0.5537E-13 0.1554E+01 39 32.30 1993.94 2002.68 0.3275E+01 0.7921E+00 41 35.55 2010.91 2004.17 0.2603E-13 0.2060E+00 43 38.60 2010.91 2004.40 0.4186E-13 -0.1667E-01 45 42.20 2019.40 2018.09 0.5861E+01 0.8100E+01 ------------------------------------------------------------------------------



A.5 – 68

-0.13241895E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "




Remark



Major parameters

Column : 8 x 8 UC 40 Beam : 14 x 5 UB 26 Plate thickness : 1" Stiffener thickness : 0.3125"

Tested by Test Id.

V - 35

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 69


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.5421E+03 0.3286E+03 3 0.27 144.52 98.78 0.5419E+03 0.4060E+03 5 0.60 280.54 244.05 0.3188E+03 0.4586E+03 7 1.00 420.80 432.27 0.3825E+03 0.4756E+03 9 1.40 582.31 620.15 0.4250E+03 0.4596E+03 11 1.70 718.33 754.45 0.5101E+03 0.4343E+03 13 2.05 837.34 900.01 0.2720E+03 0.3964E+03 15 2.25 973.36 976.92 -0.1360E+04 0.3726E+03 17 2.50 1126.38 1066.24 0.2834E+03 0.3419E+03 19 3.00 1266.64 1221.82 0.2763E+03 0.2809E+03 21 3.50 1381.40 1347.96 0.1984E+03 0.2248E+03 23 4.50 1500.42 1525.38 0.7801E+02 0.1356E+03 25 6.40 1644.94 1685.45 0.7557E+02 0.4825E+02 27 8.20 1746.95 1746.41 0.4336E+02 0.2535E+02 29 10.60 1823.45 1802.66 0.2191E+02 0.2350E+02 31 13.30 1891.46 1867.17 0.2707E+02 0.2343E+02 33 16.50 1925.46 1933.45 0.1321E+02 0.1726E+02 35 19.90 1967.96 1978.17 0.6194E+01 0.9271E+01 37 23.60 1984.97 2000.49 0.4723E+01 0.3382E+01 39 27.30 1993.48 2007.05 -0.8060E-13 0.5822E+00 41 31.10 2001.97 2007.00 0.2236E+01 -0.3970E+00 43 34.40 2001.97 2005.34 0.8338E-13 -0.5467E+00 45 38.00 2010.48 2003.50 0.1595E+01 -0.4557E+00 47 40.70 2018.98 2002.41 0.1416E+01 -0.3483E+00 49 44.30 2010.48 2001.40 0.2221E+01 -0.2216E+00 ------------------------------------------------------------------------------



A.5 – 70

-0.22627650E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark


England Fasteners: 10.9- -1"D 1 1/4" Oversize holes Material : -Fy = -ksi Fu = -ksi

Major parameters

Column : 8 x 8 UC 40 Beam : 14 x 6 3/4 UB 45 Plate thickness : 1 3/8" Stiffener thickness : 0.3125"

Tested by Test Id.

V - 36

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 71


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2359E+03 0.1226E+03 3 1.30 306.61 325.42 0.3314E+03 0.3447E+03 5 2.20 664.34 664.61 0.4145E+03 0.3982E+03 7 2.80 919.86 906.14 0.3865E+03 0.4036E+03 9 3.50 1158.32 1184.97 0.3865E+03 0.3902E+03 11 4.10 1413.84 1412.78 0.3865E+03 0.3680E+03 13 4.80 1652.32 1659.21 0.3804E+03 0.3353E+03 15 5.30 1856.74 1820.56 0.3500E+03 0.3100E+03 17 6.00 2044.12 2024.97 0.2474E+03 0.2742E+03 19 7.40 2333.63 2361.47 0.2379E+03 0.2083E+03 21 8.20 2538.14 2515.01 0.2232E+03 0.1763E+03 23 10.25 2785.10 2808.29 0.1250E+03 0.1145E+03 25 12.30 2998.02 3000.85 0.9126E+02 0.7668E+02 27 14.95 3176.88 3164.87 0.3711E+02 0.5020E+02 29 17.90 3304.67 3289.15 0.3327E+02 0.3572E+02 31 21.10 3372.77 3388.60 0.3231E+02 0.2714E+02 33 24.50 3474.91 3469.69 0.1419E+02 0.2084E+02 35 27.50 3517.48 3525.23 0.2128E+02 0.1631E+02 37 30.60 3560.26 3569.47 0.7862E+01 0.1235E+02 39 33.00 3577.28 3595.95 0.1336E+02 0.9788E+01 41 36.25 3636.86 3622.99 0.7398E+01 0.6977E+01 43 39.40 3696.44 3691.16 0.2554E+02 0.2971E+02 45 43.30 3747.52 3748.80 -0.5201E-13 -0.7656E+00 ------------------------------------------------------------------------------



A.5 – 72

0.38474808E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 37

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 73


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.3903E+03 0.4191E+03 3 0.67 260.20 295.38 0.3903E+03 0.4604E+03 5 1.20 568.48 544.17 0.8909E+03 0.4697E+03 7 1.80 865.45 824.77 0.2970E+03 0.4631E+03 9 2.60 1145.44 1185.38 0.4030E+03 0.4357E+03 11 3.35 1476.36 1498.76 0.4849E+03 0.3987E+03 13 4.05 1756.36 1764.30 0.3151E+03 0.3595E+03 15 4.65 1976.97 1969.63 0.4412E+03 0.3249E+03 17 5.40 2231.51 2197.23 0.2885E+03 0.2824E+03 19 6.55 2494.58 2486.96 0.1828E+03 0.2229E+03 21 7.90 2715.22 2747.36 0.1454E+03 0.1652E+03 23 9.70 2969.80 2991.26 0.1311E+03 0.1096E+03 25 12.60 3241.28 3227.54 0.6274E+02 0.5993E+02 27 16.20 3377.03 3391.70 0.3136E+02 0.3546E+02 29 20.00 3529.79 3504.85 0.2294E+02 0.2529E+02 31 24.10 3580.64 3593.91 0.2522E+02 0.1843E+02 33 27.90 3631.49 3653.57 0.7236E+01 0.1312E+02 35 32.00 3682.33 3697.51 0.1251E+02 0.8525E+01 37 35.30 3724.90 3720.87 0.7090E+01 0.5767E+01 39 38.20 3733.40 3734.88 0.1089E+02 0.3984E+01 41 41.00 3750.20 3744.18 -0.1225E+02 0.2733E+01 43 44.20 3750.20 3751.24 0.6207E+01 0.1742E+01 45 46.50 3767.23 3754.65 0.2128E+02 0.1247E+01 ------------------------------------------------------------------------------



A.5 – 74

0.52657486E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 38

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

8

24

cc

pc

pic

pi pi

pit

pt

ct

32

40

48

56

64



16

beam

gt

72

li

80

nc

ni

nt

A.5 – 75


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2240E+03 0.2407E+03 3 1.00 224.00 221.00 0.2542E+03 0.2337E+03 5 1.73 426.67 409.53 0.2764E+03 0.2798E+03 7 2.55 640.00 652.52 0.2489E+03 0.3100E+03 9 3.35 848.00 902.02 0.2743E+03 0.3092E+03 11 3.90 1048.00 1068.59 0.5200E+03 0.2950E+03 13 4.35 1248.00 1197.64 0.3840E+03 0.2779E+03 15 5.10 1432.00 1393.42 0.1760E+03 0.2433E+03 17 6.05 1608.00 1602.31 0.1955E+03 0.1966E+03 19 7.20 1784.00 1797.93 0.1257E+03 0.1452E+03 21 8.65 1936.00 1970.30 0.8534E+02 0.9562E+02 23 10.40 2080.00 2101.65 0.8000E+02 0.5809E+02 25 13.50 2256.00 2229.06 0.3605E+02 0.2978E+02 27 16.80 2320.00 2310.45 0.1556E+02 0.2120E+02 29 21.10 2384.00 2390.17 0.1017E+02 0.1608E+02 31 25.70 2448.00 2452.22 0.9351E+01 0.1094E+02 33 28.20 2464.00 2476.36 0.6596E+01 0.8430E+01 35 32.90 2512.00 2506.87 0.5890E+01 0.4798E+01 37 36.25 2504.00 2519.87 -0.5516E+01 0.3075E+01 39 39.70 2528.00 2528.29 0.7580E+01 0.1894E+01 41 43.40 2560.00 2533.72 0.4738E+01 0.1102E+01 43 46.90 2544.00 2536.72 0.5910E+01 0.6511E+00 ------------------------------------------------------------------------------



A.5 – 76

0.61577559E+04



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 39

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

pic

pi pi

pit

pt

ct

24

30

36

42

48



12

beam

gt

54

li

60

nc

ni

nt

A.5 – 77


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2730E+03 0.2311E+03 3 0.67 181.98 168.58 0.2730E+03 0.2833E+03 5 1.40 393.41 400.45 0.3011E+03 0.3430E+03 7 2.10 626.24 648.73 0.3747E+03 0.3598E+03 9 2.60 834.98 826.94 0.4817E+03 0.3507E+03 11 3.13 1027.68 1008.47 0.2890E+03 0.3285E+03 13 3.80 1220.36 1215.48 0.2765E+03 0.2915E+03 15 4.53 1413.05 1413.27 0.2628E+03 0.2480E+03 17 5.45 1605.74 1617.26 0.1752E+03 0.1983E+03 19 6.70 1814.48 1830.31 0.1606E+03 0.1456E+03 21 8.70 2055.34 2063.92 0.9882E+02 0.9358E+02 23 11.10 2256.05 2245.99 0.6569E+02 0.6168E+02 25 13.25 2360.43 2359.55 0.3059E+02 0.4507E+02 27 15.30 2432.69 2439.79 0.4014E+02 0.3373E+02 29 17.45 2504.95 2502.04 0.2793E+02 0.2458E+02 31 19.85 2545.09 2551.28 0.6422E+01 0.1686E+02 33 22.25 2577.20 2584.67 0.2094E+02 0.1128E+02 35 25.00 2617.34 2609.28 0.4088E+01 0.6935E+01 37 27.20 2617.34 2621.84 -0.1453E-12 0.4624E+01 39 29.10 2617.34 2629.22 0.2607E+01 0.3228E+01 41 31.70 2633.40 2635.82 0.7595E+01 0.1953E+01 43 34.60 2649.47 2640.14 0.1643E-13 0.1101E+01 45 37.10 2649.47 2642.31 0.0000E+00 0.6672E+00 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.39249167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = 0.68318500E+03 -0.83032592E+04 0.20316865E+05 -0.15759793E+05 -0.40177899E+04


A.5 – 78

0.97263586E+04



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters

Column : 8 x 8 UC 40 Beam : 8 x 5 1/4 UB 20 Plate thickness : 3/4" Stiffener thickness : 0.3125"

Tested by Test Id.

V - 40

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 79


( R : X 1/1000 radians )




A.5 – 80

-0.35800988E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 41

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 81


( R : X 1/1000 radians )




A.5 – 82

0.24352052E+05



: :

J.R.Bailey (1970) C9-L


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 42

0

90

180

270

360

450

540

630

720

810

900

tp

column

Moment ( kip-inch )


0

2

6

8

10

12

14

cc

pc

pic

pi pi

pit

pt

ct

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 83


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.9698E+02 0.3801E+02 3 0.70 67.88 70.93 0.1057E+03 0.1040E+03 5 1.30 135.76 131.99 0.1061E+03 0.1064E+03 7 1.90 195.16 202.28 0.1273E+03 0.1271E+03 9 2.20 237.58 241.32 0.1966E+03 0.1324E+03 11 2.40 284.24 267.91 0.1962E+03 0.1331E+03 13 3.00 335.15 345.57 0.1320E+03 0.1232E+03 15 3.30 381.82 381.18 0.1354E+03 0.1138E+03 17 3.80 432.73 433.64 0.1042E+03 0.9579E+02 19 4.20 475.15 469.07 0.8625E+02 0.8154E+02 21 4.80 509.09 512.27 0.5960E+02 0.6322E+02 23 5.60 560.00 555.46 0.5044E+02 0.4610E+02 25 6.60 593.94 594.94 0.3182E+02 0.3424E+02 27 7.60 623.64 625.86 0.3322E+02 0.2821E+02 29 8.20 644.84 642.03 0.3004E+02 0.2576E+02 31 9.20 666.06 666.00 0.2030E+02 0.2224E+02 33 10.30 687.28 688.40 0.1869E+02 0.1847E+02 35 11.23 704.24 704.15 0.1818E+02 0.1531E+02 ------------------------------------------------------------------------------



A.5 – 84

0.32564163E+05



: :

J.R.Bailey (1970) C9-R


1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 43

0

90

180

270

360

450

540

630

720

810

900

tp

column

Moment ( kip-inch )


0

4

12

16

20

24

28

cc

pc

pic

pi pi

pit

pt

ct

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 85


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.8484E+02 0.2097E+02 3 0.60 50.90 54.04 0.9873E+02 0.1114E+03 5 1.10 106.06 106.44 0.1052E+03 0.9788E+02 7 1.70 165.46 163.42 0.1005E+03 0.9532E+02 9 2.20 216.36 212.72 0.9757E+02 0.1022E+03 11 2.70 263.03 265.31 0.1004E+03 0.1073E+03 13 3.10 305.46 308.32 0.1032E+03 0.1070E+03 15 3.70 364.85 370.55 0.1052E+03 0.9909E+02 17 4.20 420.00 417.38 0.1019E+03 0.8774E+02 19 4.80 475.15 465.31 0.7654E+02 0.7190E+02 21 5.80 526.06 524.63 0.4299E+02 0.4778E+02 23 7.30 572.72 578.22 0.3233E+02 0.2688E+02 25 9.05 617.27 618.17 0.1414E+02 0.2092E+02 27 10.40 638.48 642.05 0.1768E+02 0.1383E+02 29 11.60 661.82 658.93 0.2121E+02 0.1416E+02 31 13.05 683.03 678.97 0.9981E+01 0.1320E+02 33 14.70 700.00 698.66 0.1061E+02 0.1044E+02 35 16.30 710.60 712.62 0.2655E+01 0.6956E+01 37 17.95 716.97 721.10 0.4991E+01 0.3382E+01 39 19.50 723.34 724.02 0.3034E+01 0.4779E+00 41 21.20 725.46 722.60 0.0000E+00 -0.2032E+01 ------------------------------------------------------------------------------



A.5 – 86

0.54760414E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters

Column : 8 x 8 UC 40 Beam : 12 x 5 UB 32 Plate thickness : 13/16" Stiffener thickness : 0.3125"

Tested by Test Id.

V - 44

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 87


( R : X 1/1000 radians )




A.5 – 88

0.13612022E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 45

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 89


( R : X 1/1000 radians )




A.5 – 90

0.71354482E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 46

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

1

3

4

5

6

7

8

cc

pc

pic

pi pi

pit

pt

ct



2

beam

gt

9

li

10

nc

ni

nt

A.5 – 91


( R : X 1/1000 radians )


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.46143422E+03 -0.43921227E+04 0.13090131E+05 -0.57413758E+04 -0.20897500E+05 Rj0 = 0.8000 4.0000 5.8000 RKj = 0.74035942E+02 -0.11633230E+03 0.60741891E+02


A.5 – 92

0.18698841E+05



: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 47

0 0.0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0.9

2.7

3.6

4.5

5.4

6.3

cc

pc

pic

pi pi

pit

pt

ct

7.2



1.8

beam

gt

8.1

li

9.0

nc

ni

nt

A.5 – 93


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2391E+03 0.3903E+03 2 0.27 63.76 65.44 0.2391E+03 0.1972E+03 3 0.53 127.51 123.74 0.2391E+03 0.2438E+03 4 0.80 191.27 193.02 0.2563E+03 0.2690E+03 5 1.00 245.11 246.85 0.2692E+03 0.2675E+03 6 1.20 298.95 299.61 0.2692E+03 0.2598E+03 7 1.40 352.79 350.86 0.2553E+03 0.2532E+03 8 1.65 412.30 413.72 0.2380E+03 0.2508E+03 9 1.90 471.80 476.75 0.2841E+03 0.2543E+03 10 2.05 518.56 515.16 0.3117E+03 0.2580E+03 11 2.20 565.31 554.16 0.2783E+03 0.2621E+03 12 2.40 612.07 607.08 0.2338E+03 0.2669E+03 13 2.60 658.82 660.80 0.2232E+03 0.2700E+03 14 2.80 701.33 714.90 0.2125E+03 0.2706E+03 15 3.00 743.83 768.85 0.3340E+03 0.2685E+03 16 3.15 807.59 808.88 0.4250E+03 0.2650E+03 17 3.30 871.34 848.28 0.3485E+03 0.2601E+03 18 3.55 926.60 911.99 0.2210E+03 0.2490E+03 19 3.80 981.86 972.53 0.1927E+03 0.2349E+03 20 4.00 1015.87 1018.25 0.1700E+03 0.2222E+03 21 4.20 1049.87 1061.33 0.1700E+03 0.2085E+03 22 4.40 1083.88 1101.62 0.2348E+03 0.1943E+03 23 4.55 1126.38 1129.96 0.2834E+03 0.1836E+03 24 4.70 1168.88 1156.70 0.2105E+03 0.1729E+03 25 4.93 1191.55 1186.79 0.9714E+02 0.1208E+03 26 5.17 1214.22 1213.14 0.9714E+02 0.1051E+03 27 5.40 1236.89 1235.90 0.8565E+02 0.9016E+02 28 5.70 1258.14 1260.25 0.7084E+02 0.7245E+02 29 6.00 1279.39 1279.55 0.7084E+02 0.5654E+02 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.11667500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.60812984E+03 -0.77200477E+04 0.29620777E+05 -0.37101265E+05 0.19943345E+04 Rj0 = 4.7000 RKj = -0.35622686E+02


A.5 – 94

0.14075023E+05



: :



2.5000" 3.5000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 48

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

8

24

32

cc

pc

pic

pi pi

pit

pt

ct

48

56

64


40

Material : : :


16

beam

gt

72

li

80

nc

ni

nt

A.5 – 95


A3 = P3 =

2.040000 5

K = Q1 =

0.002824 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2540E+03 0.1978E+03 0.2798E+03 3 0.73 186.31 142.39 199.45 0.2541E+03 0.1862E+03 0.2740E+03 5 1.40 398.03 255.90 388.20 0.3952E+03 0.1511E+03 0.2925E+03 7 2.10 618.22 346.63 598.14 0.2541E+03 0.1096E+03 0.3052E+03 9 2.95 838.41 424.25 857.42 0.2635E+03 0.7618E+02 0.3015E+03 11 3.70 1067.07 474.34 1077.51 0.3670E+03 0.5882E+02 0.2836E+03 13 4.45 1278.79 513.99 1280.69 0.2258E+03 0.4767E+02 0.2573E+03 15 5.40 1507.45 554.56 1507.14 0.2541E+03 0.3841E+02 0.2191E+03 17 6.45 1727.64 591.12 1715.14 0.1694E+03 0.3168E+02 0.1776E+03 19 7.70 1905.49 627.13 1909.63 0.1210E+03 0.2628E+02 0.1350E+03 21 9.90 2125.67 677.83 2143.86 0.8760E+02 0.2034E+02 0.8252E+02 23 13.30 2345.86 737.38 2347.51 0.4256E+02 0.1523E+02 0.4357E+02 25 17.70 2481.36 795.69 2494.20 0.3143E+02 0.1163E+02 0.2622E+02 27 21.20 2599.92 833.09 2573.85 0.1652E+02 0.9850E+01 0.1971E+02 29 25.10 2650.74 868.63 2639.65 0.1907E+02 0.8454E+01 0.1422E+02 31 29.60 2684.62 903.93 2691.79 0.9834E+01 0.7297E+01 0.9186E+01 33 32.35 2710.02 923.37 2713.66 0.6778E+01 0.6742E+01 0.6804E+01 35 35.50 2718.49 943.61 2731.61 0.4830E+01 0.6218E+01 0.4697E+01 37 39.20 2735.42 965.63 2745.54 0.1044E-12 0.5702E+01 0.2949E+01 39 43.40 2769.30 988.54 2755.05 0.1756E+01 0.5220E+01 0.1684E+01 41 47.40 2786.24 1008.63 2760.22 -0.5136E+01 0.4838E+01 0.9632E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.49584167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = 0.60311678E+03 -0.41210082E+04 -0.59860340E+04 0.46259627E+05 -0.65095319E+05



A.5 – 96


: :



2.5000" 3.5000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 49

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

8

24

32

cc

pc

pic

pi pi

pit

pt

ct

48

56

64


40

Material : : :


16

beam

gt

72

li

80

nc

ni

nt

A.5 – 97


A3 = P3 =

2.040000 5

K = Q1 =

0.002824 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4137E+03 0.1978E+03 0.2935E+03 3 0.70 289.58 136.17 267.75 0.4015E+03 0.1873E+03 0.4415E+03 5 1.40 562.13 255.91 589.15 0.4603E+03 0.1511E+03 0.4632E+03 7 1.90 817.64 323.62 816.41 0.4723E+03 0.1204E+03 0.4426E+03 9 2.50 1073.16 386.66 1070.01 0.4166E+03 0.9153E+02 0.4008E+03 11 3.00 1277.57 427.99 1260.44 0.3417E+03 0.7475E+02 0.3607E+03 13 3.80 1464.95 480.14 1523.31 0.4046E+03 0.5705E+02 0.2973E+03 15 4.30 1720.45 506.70 1662.78 0.4088E+03 0.4956E+02 0.2612E+03 17 5.30 1924.87 550.68 1892.14 0.1696E+03 0.3921E+02 0.2001E+03 19 6.50 2078.17 592.70 2097.82 0.1246E+03 0.3142E+02 0.1460E+03 21 8.20 2282.58 639.84 2300.70 0.1077E+03 0.2462E+02 0.9722E+02 23 9.80 2435.89 675.76 2433.18 0.8729E+02 0.2055E+02 0.7070E+02 25 13.70 2657.34 743.39 2641.47 0.3996E+02 0.1480E+02 0.4116E+02 27 17.90 2793.61 798.00 2781.54 0.2891E+02 0.1151E+02 0.2677E+02 29 21.30 2853.23 834.07 2858.22 0.7095E+01 0.9808E+01 0.1870E+02 31 24.70 2912.86 865.22 2910.91 0.1549E+02 0.8577E+01 0.1260E+02 33 28.60 2946.92 896.52 2949.77 0.4733E+01 0.7523E+01 0.7668E+01 35 32.40 2946.92 923.55 2972.55 0.9961E+01 0.6737E+01 0.4560E+01 37 36.50 2980.99 949.75 2986.70 0.5307E+01 0.6068E+01 0.2525E+01 39 40.20 2998.02 971.27 2993.88 -0.4481E+01 0.5579E+01 0.1450E+01 41 44.20 3015.06 992.68 2998.22 0.7258E+01 0.5139E+01 0.7831E+00 43 47.20 3015.06 1007.88 3000.09 0.0000E+00 0.4852E+01 0.4887E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.48083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = -0.40678379E+03 -0.27634475E+04 0.93328384E+04 0.15024946E+04 -0.19163554E+05



A.5 – 98


: :



1) 2)

-" -" -" X 1

---

nc = 2 X

pc = pic=

" "

------------------------------




Remark



Major parameters


Tested by Test Id.

V - 50

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 99


( R : X 1/1000 radians )




A.5 – 100

0.90827187E+05



: :


© 2011 J. Ross Publishing, Inc. -" -" -" X 1

---

nc = 2 X

pc = pic= 1

" "

------------------------------




1) 2)

End plate extended on tension side only. ct = -" pt = 4.6250" li = cc = -" pit= -" pi = gt = -" gi = -" gc = tp = 1.1400" nt = 2 X 2 ni = 2

Remark


Major parameters


Tested by Test Id.

V - 51

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 101


( R : X 1/1000 radians )




A.5 – 102

0.87384835E+05



: :



5.0000"


End plate extended on tension side only. Hsfg bolts used either side of beam tension flange.


1) 2)


Remark

England

Fasteners: 10.9- -1 1/8"D 1 7/16" Oversize holes Material : -Fy = -ksi Fu = -ksi



Tested by Test Id.

V - 52

0

700

1400

2100

2800

3500

4200

4900

5600

6300

7000

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

pic

pi pi

pit

pt

ct

36

42

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 103


A3 = P3 =

2.040000 5

K = Q1 =

0.001201 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 104


: :



7.0078"

------------------------------


End plate extended on tension and compression side. 16 mm web doubler plates on both sides of column used.


1) 2)

End plate extended on both sides. ct = -" pt = 7.0078" li = -" cc = -" gt = 5.5118" gc = 5.5118" tp = 1.2600" nt = 2 X 2 nc = 2 X 2

Remark

New-Zealand


N.D.Johnstone & W.R.Walpole (1981) TEST 1-L

Column : 250 UC 89 Beam : 310 UB 46 Plate thickness : 32 mm Stiffener thickness : 0.6300"

Tested by Test Id.

V - 53

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

cc

pc

li

pt

ct

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.5 – 105


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.2014E+04 0.8349E+03 3 0.10 201.36 81.59 0.1745E+04 0.7973E+03 5 0.60 402.71 437.91 0.3905E+03 0.6348E+03 7 1.13 604.07 739.06 0.3776E+03 0.5005E+03 9 1.35 824.30 842.51 -0.2391E+04 0.4551E+03 11 1.50 1038.25 908.59 0.4719E+03 0.4263E+03 13 2.30 1239.60 1197.28 0.1783E+03 0.3031E+03 15 3.50 1440.95 1484.53 0.1573E+03 0.1864E+03 17 4.65 1636.02 1658.15 0.1831E+03 0.1213E+03 19 6.05 1805.92 1793.68 0.8143E+02 0.7705E+02 21 9.70 1988.40 1983.43 0.3627E+02 0.3747E+02 23 14.65 2126.83 2135.36 0.2375E+02 0.2579E+02 25 19.50 2233.81 2240.48 0.2002E+02 0.1757E+02 27 24.00 2303.02 2303.64 0.1094E+02 0.1077E+02 29 28.60 2347.07 2340.96 0.8207E+01 0.5813E+01 31 33.00 2372.24 2367.90 0.2997E+01 0.6875E+01 33 38.70 2391.11 2400.88 0.5651E+01 0.4966E+01 35 43.90 2422.57 2424.55 0.3309E+01 0.4246E+01 37 49.40 2441.45 2447.01 0.3450E+01 0.3973E+01 39 55.45 2466.62 2470.76 0.5354E+01 0.3902E+01 41 61.30 2504.38 2493.59 0.4482E+01 0.3906E+01 43 66.10 2516.96 2512.37 0.2711E+01 0.3921E+01 45 70.60 2529.54 2530.05 0.2981E+01 0.3934E+01 47 74.60 2542.13 2545.80 0.3147E+01 0.3943E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.63416667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.18662481E+03 0.73369929E+03 0.10452855E+05 -0.28148011E+05 0.26010953E+05 Rj0 = 30.9000 RKj = 0.39636409E+01


A.5 – 106

-0.68637164E+04



: :



7.0078"

------------------------------




1) 2)


Remark

New-Zealand


N.D.Johnstone & W.R.Walpole (1981) TEST 1-R


Tested by Test Id.

V - 54

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

cc

pc

li

pt

ct

88


gc


22

beam

gt

99

lp

110

nc

ni

nt

A.5 – 107


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.9567E+03 0.1172E+04 3 0.24 229.61 258.20 0.9567E+03 0.9862E+03 5 0.48 459.23 476.04 0.9567E+03 0.8341E+03 7 0.75 693.89 681.79 0.7990E+03 0.6951E+03 9 1.10 920.98 899.36 0.5362E+03 0.5547E+03 11 1.55 1116.53 1117.65 0.3533E+03 0.4232E+03 13 2.25 1337.32 1363.63 0.2944E+03 0.2911E+03 15 3.40 1602.25 1624.54 0.1892E+03 0.1772E+03 17 4.75 1829.35 1815.94 0.1456E+03 0.1138E+03 19 7.25 2012.28 2024.60 0.4773E+02 0.6089E+02 21 12.30 2226.76 2221.45 0.2681E+02 0.2535E+02 23 16.30 2302.45 2302.08 0.1537E+02 0.1586E+02 25 20.70 2352.91 2355.06 0.1092E+02 0.8462E+01 27 25.60 2403.38 2380.14 0.7854E+01 0.2192E+01 29 30.10 2428.62 2433.76 0.7241E+01 0.1041E+02 31 34.40 2466.47 2475.00 0.7735E+01 0.9023E+01 33 38.10 2491.69 2507.74 0.8802E+01 0.8779E+01 35 42.60 2542.16 2547.79 0.1233E+02 0.9092E+01 37 46.40 2592.62 2583.19 0.1223E+02 0.9554E+01 39 51.00 2643.08 2628.48 0.1065E+02 0.1012E+02 41 55.90 2693.56 2679.36 0.6384E+01 0.1062E+02 43 60.30 2706.17 2726.88 0.7097E+01 0.1095E+02 45 67.50 2756.64 2749.51 -0.3614E+01 -0.4702E+01 47 73.30 2718.79 2722.71 -0.6526E+01 -0.4556E+01 ------------------------------------------------------------------------------



A.5 – 108

-0.33122459E+05



: :



7.0078"

------------------------------




1) 2)


Remark

New-Zealand




Tested by Test Id.

V - 55

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

cc

pc

li

pt

ct

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.5 – 109


( R : X 1/1000 radians )




A.5 – 110

-0.39486424E+05



: :



7.0078"

------------------------------




1) 2)


Remark

New-Zealand




Tested by Test Id.

V - 56

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

cc

pc

li

pt

ct

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.5 – 111


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.5642E+03 0.7700E+03 3 0.40 225.70 258.12 0.5642E+03 0.5371E+03 5 0.80 451.39 440.67 0.5642E+03 0.3870E+03 7 1.43 648.77 639.13 0.1951E+03 0.2568E+03 9 2.30 817.82 827.10 0.1908E+03 0.1909E+03 11 3.30 1003.78 1007.66 0.1860E+03 0.1751E+03 13 4.33 1181.30 1186.36 0.1585E+03 0.1705E+03 15 5.40 1350.36 1363.02 0.1713E+03 0.1592E+03 17 6.50 1553.23 1527.77 0.1523E+03 0.1392E+03 19 7.97 1713.83 1708.21 0.1095E+03 0.1064E+03 21 10.95 1901.91 1934.43 0.4790E+02 0.4958E+02 23 15.85 2060.41 2066.54 0.1914E+02 0.1422E+02 25 21.45 2142.82 2133.38 0.1075E+02 0.1164E+02 27 24.50 2174.52 2169.06 0.2914E+00 0.1160E+02 29 30.30 2225.23 2229.72 0.7562E+01 0.8846E+01 31 36.30 2263.27 2270.62 0.5036E+01 0.4860E+01 33 43.70 2288.64 2292.91 0.4054E+01 0.1541E+01 35 49.30 2314.00 2297.80 0.3019E+00 0.3623E+00 37 55.30 2288.64 2292.12 -0.2818E+01 -0.1148E+01 39 61.50 2280.18 2284.53 -0.1364E+01 -0.1260E+01 41 68.35 2282.30 2275.99 0.1691E+01 -0.1220E+01 43 74.35 2301.32 2298.60 0.5635E+01 0.3799E+01 45 79.90 2314.00 2319.82 0.0000E+00 0.3847E+01 ------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.71583333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.39545646E+04 -0.30542232E+05 0.96307069E+05 -0.14075392E+06 0.98516720E+05 Rj0 = 49.3000 68.3500 RKj = -0.10165896E+01 0.49572881E+01


A.5 – 112

-0.25189553E+05



: :



4.0160"

------------------------------




1) 2)


Remark

New-Zealand




Tested by Test Id.

V - 57

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

20

60

80

cc

pc

li

pt

ct

lp

nc

ni

nt

100 120 140 160 180 200


gc


40

beam

gt

A.5 – 113


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.3695E+03 0.5008E+03 3 0.47 172.42 210.75 0.3695E+03 0.4064E+03 5 0.87 351.15 360.14 0.5552E+03 0.3429E+03 7 1.20 536.18 467.05 0.4604E+03 0.2999E+03 9 2.20 712.82 717.96 0.1766E+03 0.2103E+03 11 3.23 885.24 905.70 0.1577E+03 0.1580E+03 13 4.30 1053.46 1056.44 0.1415E+03 0.1274E+03 15 5.70 1221.67 1217.15 0.1202E+03 0.1043E+03 17 7.85 1419.32 1416.92 0.7831E+02 0.8289E+02 19 10.85 1627.49 1629.90 0.6105E+02 0.5976E+02 21 15.60 1823.04 1843.35 0.3154E+02 0.3233E+02 23 24.70 2037.52 2023.50 0.1287E+02 0.1261E+02 25 31.60 2100.59 2096.73 0.7544E+01 0.9013E+01 27 41.00 2151.06 2162.18 0.4928E+01 0.4815E+01 29 52.50 2201.52 2189.29 0.3890E+01 0.2419E+00 31 63.60 2239.37 2235.09 0.2387E+01 0.3307E+01 33 71.00 2251.99 2258.12 0.2573E+01 0.3019E+01 35 83.50 2302.45 2297.66 0.3232E+01 0.3412E+01 37 93.17 2327.68 2333.03 0.2610E+01 0.3903E+01 39 103.65 2371.84 2376.42 0.5583E+01 0.4353E+01 41 114.05 2409.69 2402.78 0.1328E+01 0.3196E+00 43 123.30 2411.79 2406.61 -0.9342E+00 0.4949E+00 45 132.30 2403.38 2411.58 -0.9342E+00 0.6013E+00 ------------------------------------------------------------------------------



A.5 – 114

-0.54989907E+05



: :



4.0160"

------------------------------




1) 2)


Remark

New-Zealand




Tested by Test Id.

V - 58

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

8

24

cc

pc

li

pt

ct

32

40

48

56

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.5 – 115


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.3985E+03 0.5581E+03 3 0.40 159.41 201.36 0.3985E+03 0.4500E+03 5 0.70 310.42 325.17 0.7131E+03 0.3770E+03 7 0.90 453.05 396.19 0.6241E+03 0.3340E+03 9 1.80 654.41 629.39 0.1847E+03 0.1996E+03 11 3.50 843.18 882.13 0.1290E+03 0.1225E+03 13 4.90 1044.54 1047.73 0.1431E+03 0.1159E+03 15 5.90 1187.16 1161.82 0.1426E+03 0.1116E+03 17 7.65 1346.57 1343.68 0.7048E+02 0.9447E+02 19 10.25 1522.76 1546.00 0.6525E+02 0.6167E+02 21 13.40 1686.37 1694.37 0.4195E+02 0.3585E+02 23 17.30 1818.50 1807.80 0.2697E+02 0.2478E+02 25 21.27 1904.50 1897.84 0.1573E+02 0.2087E+02 27 25.00 1963.22 1968.89 0.1433E+02 0.1704E+02 29 29.67 2021.95 2035.76 0.1258E+02 0.1163E+02 31 34.13 2072.29 2077.34 0.9832E+01 0.7196E+01 33 38.40 2114.24 2101.25 0.4500E+01 0.4214E+01 35 42.00 2114.24 2107.86 -0.1166E+01 0.1073E+01 37 45.60 2105.85 2109.69 -0.2331E+01 0.2367E-01 39 48.50 2114.24 2108.92 0.1144E+02 -0.5179E+00 ------------------------------------------------------------------------------



A.5 – 116

0.75464810E+05



: :



4.5270"

------------------------------




1) 2)


Remark

New-Zealand




Tested by Test Id.

V - 59

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

16

48

64

80

96

cc

pc

li

pt

ct

lp

nc

ni

nt

112 128 144 160


gc


32

beam

gt

A.5 – 117


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.7317E+03 0.4921E+03 3 0.27 195.06 122.18 0.7314E+03 0.4260E+03 5 1.05 410.58 396.48 0.1815E+03 0.2860E+03 7 2.23 610.36 659.01 0.1534E+03 0.1721E+03 9 3.30 773.96 813.15 0.1750E+03 0.1225E+03 11 4.40 991.06 931.86 0.1527E+03 0.9617E+02 13 6.50 1132.63 1106.05 0.6011E+02 0.7303E+02 15 9.80 1293.08 1313.62 0.5024E+02 0.5402E+02 17 12.90 1453.55 1459.45 0.4556E+02 0.4069E+02 19 17.60 1623.44 1617.18 0.3205E+02 0.2787E+02 21 24.45 1783.90 1777.38 0.2137E+02 0.2030E+02 23 30.55 1897.16 1891.34 0.1642E+02 0.1722E+02 25 37.45 1991.54 1998.88 0.1094E+02 0.1390E+02 27 44.75 2067.05 2086.77 0.9807E+01 0.1020E+02 29 52.55 2156.72 2152.27 0.1314E+02 0.6724E+01 31 60.15 2227.51 2214.44 0.5172E+01 0.1001E+02 33 68.40 2279.42 2288.95 0.7182E+01 0.8195E+01 35 77.00 2345.50 2354.15 0.8259E+01 0.7075E+01 37 84.40 2392.69 2384.77 0.4163E+01 0.7852E+00 39 92.60 2397.40 2389.67 -0.1966E+01 0.4443E+00 41 100.10 2387.96 2392.31 0.1543E-13 0.2764E+00 ------------------------------------------------------------------------------



A.5 – 118

0.37711768E+05



: :



4.5270"

------------------------------




1) 2)


Remark

New-Zealand




Tested by Test Id.

V - 60

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

8

24

cc

pc

li

pt

ct

32

40

48

56

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.5 – 119


( R : X 1/1000 radians )

-----------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. M.Expo. Expri. M.Expo. -----------------------------------------------------------------------------1 0.00 0.00 0.00 0.1346E+03 0.4327E+02 3 1.20 161.51 152.87 0.1346E+03 0.1644E+03 5 2.40 323.02 343.37 0.1419E+03 0.1463E+03 7 3.47 481.36 485.13 0.1484E+03 0.1205E+03 9 4.70 630.20 620.72 0.9953E+02 0.1013E+03 11 6.10 769.55 753.67 0.8934E+02 0.8987E+02 13 7.83 902.56 901.47 0.7674E+02 0.8098E+02 15 9.80 1032.40 1051.03 0.5758E+02 0.7090E+02 17 12.00 1159.08 1193.58 0.7816E+02 0.5864E+02 19 13.27 1273.09 1263.46 0.9000E+02 0.5176E+02 21 15.55 1391.84 1368.69 0.3743E+02 0.4076E+02 23 19.50 1505.85 1500.18 0.2272E+02 0.2686E+02 25 24.00 1591.36 1597.26 0.1511E+02 0.1712E+02 27 28.00 1640.44 1654.00 0.8798E+01 0.1161E+02 29 31.60 1672.12 1689.20 0.9104E+01 0.8135E+01 31 36.27 1716.45 1719.38 0.9501E+01 0.5015E+01 33 40.27 1744.95 1735.64 0.3799E+01 0.3232E+01 35 43.60 1757.62 1744.60 -0.3649E+01 0.2203E+01 37 47.90 1700.62 1703.03 -0.1326E+02 -0.1008E+02 ------------------------------------------------------------------------------



A.5 – 120

0.27835092E+05




1) 2)

li pi gc ni

= 19.7500" = 14.5000" = 5.5000" = 2 X 2

------------------------------


3

3.5000" 2.6250"

nc = 2 X

End plate was stiffened in the plane of beam web. Test was conducted for beam-to-beam connection.


Remark

End plate extended on both sides. ct = 4.1250" pt = 3.5000" cc = 4.1250" pit= 2.6250" gt = 5.5000" gi = 5.5000" tp = 0.7500" nt = 2 X 3 pc = pic=

Fasteners: A325- -7/8"D 15/16" Oversize holes Material : A36 Fy = 38.70 ksi Fu = -ksi

Column : -Beam : W24x100 Plate thickness : 3/4" Stiffener thickness : 0.6250"

Major parameters

U.S.A

: :

A.Mazroi (1983) EP3

Tested by Test Id.

V - 61

0 0.0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

tp

column

Moment ( kip-inch )


0.6

1.8

cc

pc

li

pt

ct

2.4

3.0

3.6

4.2

4.8


gc


1.2

beam

gt

5.4

lp

6.0

nc

ni

nt

A.5 – 121


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 122



1) 2)

li pi gc ni

= 19.7500" = 14.5000" = 5.5000" = 2 X 2

------------------------------


3

3.5000" 2.6250"

nc = 2 X

End plate was stiffened in the plane of beam web. Test was conducted for beam-to-beam connection.


Remark



Column : -Beam : W24x100 Plate thickness : 1" Stiffener thickness : 0.6250"

Major parameters

U.S.A

: :

A.Mazroi (1983) EP4

Tested by Test Id.

V - 62

0 0.0

1100

2200

3300

4400

5500

6600

7700

8800

9900

11000

tp

column

Moment ( kip-inch )


0.4

1.2

cc

pc

li

pt

ct

1.6

2.0

2.4

2.8

3.2


gc


0.8

beam

gt

3.6

lp

4.0

nc

ni

nt

A.5 – 123


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.16533333E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.69938572E+04 -0.72635585E+05 0.25505486E+06 -0.39084089E+06 0.25726413E+06 Rj0 = 0.0000 RKj = 0.13920519E+04



A.5 – 124



1) 2)

li pi gc ni

= 22.3901" = 17.0567" = 5.5000" = 2 X 2 nc = 2 X

3

3.9300" 2.6667"

------------------------------


End plate was stiffened in the plane of beam web by an end-plate. Test was conducted for beam-to-beam connection.


Remark


Fasteners: A325- -1"D 1 1/16" Oversize holes Material : A36 Fy = 38.20 ksi Fu = -ksi

Column : -Beam : W27x114 Plate thickness : 1" Stiffener thickness : 0.6250"

Major parameters

U.S.A

: :

A.Mazroi (1983) EP5

Tested by Test Id.

V - 63

0 0.0

1250

2500

3750

5000

6250

7500

8750

10000

11250

12500

tp

column

Moment ( kip-inch )


0.3

0.9

cc

pc

li

pt

ct

1.2

1.5

1.8

2.1

2.4


gc


0.6

beam

gt

2.7

lp

3.0

nc

ni

nt

A.5 – 125


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3438E+05 0.1956E+04 0.3459E+05 2 0.01 388.48 22.10 401.80 0.3423E+05 0.1956E+04 0.3540E+05 3 0.02 776.95 44.39 789.33 0.3423E+05 0.1956E+04 0.3232E+05 4 0.03 1165.43 66.49 1134.34 0.3000E+05 0.1956E+04 0.2882E+05 5 0.05 1522.83 95.24 1531.00 0.2440E+05 0.1956E+04 0.2542E+05 6 0.06 1880.24 123.80 1886.56 0.2440E+05 0.1956E+04 0.2349E+05 7 0.08 2237.64 152.55 2223.67 0.2289E+05 0.1956E+04 0.2247E+05 8 0.10 2628.07 188.74 2631.48 0.2110E+05 0.1957E+04 0.2164E+05 9 0.12 3018.49 224.94 3023.33 0.2017E+05 0.1957E+04 0.2068E+05 10 0.14 3428.71 267.02 3452.20 0.1908E+05 0.1958E+04 0.1914E+05 11 0.16 3838.92 309.10 3844.09 0.1779E+05 0.1958E+04 0.1728E+05 12 0.18 4275.41 361.97 4278.10 0.1617E+05 0.1959E+04 0.1490E+05 13 0.21 4711.90 414.87 4652.26 0.1384E+05 0.1960E+04 0.1291E+05 14 0.25 5128.01 493.27 5127.19 0.1040E+05 0.1962E+04 0.1107E+05 15 0.29 5544.12 571.75 5554.30 0.1024E+05 0.1964E+04 0.1045E+05 16 0.34 6006.40 662.11 6035.39 0.1005E+05 0.1967E+04 0.1055E+05 17 0.38 6468.67 752.59 6527.35 0.1130E+05 0.1970E+04 0.1082E+05 18 0.42 6970.91 832.40 6966.44 0.1240E+05 0.1974E+04 0.1082E+05 19 0.47 7473.16 912.33 7398.91 0.1045E+05 0.1977E+04 0.1048E+05 20 0.50 7798.76 986.88 7783.78 0.8648E+04 0.1981E+04 0.9892E+04 21 0.54 8124.36 1061.37 8141.28 0.8648E+04 0.1985E+04 0.9096E+04 22 0.58 8449.96 1136.21 8466.99 0.8591E+04 0.1989E+04 0.8168E+04 23 0.62 8812.91 1220.77 8791.26 0.8540E+04 0.1995E+04 0.8209E+04 24 0.66 9175.87 1305.54 9116.77 0.7256E+04 0.2000E+04 0.7117E+04 25 0.76 9587.79 1489.58 9672.44 0.4477E+04 0.2014E+04 0.5047E+04 26 0.85 9999.70 1677.09 10062.86 0.4477E+04 0.2030E+04 0.3535E+04 27 0.94 10411.62 1863.85 10338.85 0.4477E+04 0.2048E+04 0.2541E+04 --------------------------------------------------------------------------------------------------




A.5 – 126



Remark

1) 2)

li pi gc ni

= 21.3900" = 15.3900" = 6.5000" = 2 X 2 nc = 2 X

3

4.9300" 3.0000"

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 345.52 0.00 3 1036.56 0.00 4 1568.21 0.01 5 2206.22 0.04 6 2764.52 0.05 7 3336.04 0.07 8 3934.28 0.10 9 4452.82 0.13 10 4984.57 0.16 11 5649.32 0.21 12 6181.27 0.25 13 6646.81 0.32 14 7258.60 0.40 15 7737.46 0.47 16 8181.10 0.56 17 8575.94 0.65 18 8926.51 0.74 19 9281.60 0.84 20 9494.81 0.93 21 9734.66 1.03 22 10001.15 1.13 ------------------------------




Column : -Beam : W27x114 Plate thickness : 1 1/4" Stiffener thickness : 0.6250"

Major parameters

U.S.A

: :

A.Mazroi (1983) EP6

Tested by Test Id.

V - 64

0 0.0

1250

2500

3750

5000

6250

7500

8750

10000

11250

12500

tp

column

Moment ( kip-inch )


0.4

1.2

cc

pc

li

pt

ct

1.6

2.0

2.4

2.8

3.2


gc


0.8

beam

gt

3.6

lp

4.0

nc

ni

nt

A.5 – 127


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.95250000E-02 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.74280345E+04 -0.23899132E+05 0.50597183E+04 0.12323549E+06 -0.22025181E+06 Rj0 = 0.0000 RKj = 0.25995267E+04



A.5 – 128



1) 2)

li pi gc ni

= 19.3100" = 13.3100" = 5.5000" = 2 X 2 nc = 2 X

3

4.4700" 3.0000"

------------------------------




Remark


Fasteners: A325- -1 1/8"D 1 1/4" Oversize holes Material : A36 Fy = 33.00 ksi Fu = -ksi


Major parameters

U.S.A

: :

A.Mazroi (1983) EP7

Tested by Test Id.

V - 65

0 0.0

1450

2900

4350

5800

7250

8700

10150

11600

13050

14500

tp

column

Moment ( kip-inch )


0.4

1.2

cc

pc

li

pt

ct

1.6

2.0

2.4

2.8

3.2


gc


0.8

beam

gt

3.6

lp

4.0

nc

ni

nt

A.5 – 129


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3607E+05 0.2329E+04 0.4971E+05 2 0.01 396.75 25.62 477.49 0.3607E+05 0.2329E+04 0.3632E+05 3 0.02 793.50 51.24 825.39 0.3607E+05 0.2329E+04 0.2787E+05 4 0.03 1190.24 76.86 1106.56 0.3167E+05 0.2329E+04 0.2380E+05 5 0.06 1758.68 140.91 1721.43 0.2067E+05 0.2329E+04 0.2210E+05 6 0.09 2327.11 204.96 2344.99 0.2115E+05 0.2330E+04 0.2323E+05 7 0.11 2800.82 256.22 2859.92 0.2153E+05 0.2330E+04 0.2343E+05 8 0.13 3274.54 307.49 3368.70 0.2693E+05 0.2331E+04 0.2268E+05 9 0.14 3633.01 335.46 3636.75 0.2987E+05 0.2331E+04 0.2196E+05 10 0.16 3991.48 363.44 3895.08 0.2555E+05 0.2332E+04 0.2107E+05 11 0.18 4363.74 411.24 4309.58 0.1816E+05 0.2333E+04 0.1933E+05 12 0.20 4736.00 459.06 4687.02 0.1632E+05 0.2334E+04 0.1749E+05 13 0.23 5155.89 531.40 5187.16 0.1354E+05 0.2335E+04 0.1483E+05 14 0.26 5575.78 603.79 5610.82 0.1250E+05 0.2337E+04 0.1258E+05 15 0.30 6036.50 700.77 6083.99 0.1110E+05 0.2340E+04 0.1037E+05 16 0.34 6497.22 797.87 6482.98 0.1008E+05 0.2343E+04 0.8978E+04 17 0.39 6958.24 920.87 6926.81 0.8096E+04 0.2348E+04 0.8050E+04 18 0.46 7419.67 1069.94 7420.96 0.7305E+04 0.2354E+04 0.7586E+04 19 0.52 7908.14 1226.48 7916.75 0.7345E+04 0.2362E+04 0.7332E+04 20 0.59 8396.62 1383.56 8394.82 0.7184E+04 0.2371E+04 0.7026E+04 21 0.64 8735.87 1497.37 8725.14 0.6817E+04 0.2378E+04 0.6726E+04 22 0.74 9374.06 1740.92 9368.20 0.5793E+04 0.2396E+04 0.5917E+04 23 0.85 9938.09 1997.29 9951.56 0.4887E+04 0.2417E+04 0.4993E+04 24 0.95 10398.34 2243.38 10418.97 0.4272E+04 0.2441E+04 0.4214E+04 25 1.05 10788.62 2482.97 10796.79 0.3877E+04 0.2467E+04 0.3627E+04 26 1.15 11188.21 2749.37 11161.13 0.3337E+04 0.2499E+04 0.3150E+04 27 1.27 11524.91 3038.10 11499.71 0.2626E+04 0.2537E+04 0.2815E+04 28 1.39 11798.72 3342.58 11823.40 0.2282E+04 0.2583E+04 0.2598E+04 --------------------------------------------------------------------------------------------------




A.5 – 130



1) 2)

li pi gc ni

= 19.3100" = 13.3100" = 5.5000" = 2 X 2 nc = 2 X

3

4.4700" 3.0000"

------------------------------




Remark




Major parameters

U.S.A

: :

A.Mazroi (1983) EP7 With Shim

Tested by Test Id.

V - 66

0 0.0

1800

3600

5400

7200

9000

10800

12600

14400

16200

18000

tp

column

Moment ( kip-inch )


0.5

1.5

cc

pc

li

pt

ct

2.0

2.5

3.0

3.5

4.0


gc


1.0

beam

gt

4.5

lp

5.0

nc

ni

nt

A.5 – 131


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.23758333E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.26969202E+04 -0.13697045E+06 0.79073889E+06 -0.16426884E+07 0.15307921E+07 Rj0 = 0.9300 RKj = 0.14929365E+04



A.5 – 132



1) 2)

li pi gc ni

= 18.3100" = 11.5600" = 6.5000" = 2 X 2 nc = 2 X

3

5.4700" 3.3750"

------------------------------




Remark




Major parameters

U.S.A

: :

A.Mazroi (1983) EP8

Tested by Test Id.

V - 67

0 0.0

1600

3200

4800

6400

8000

9600

11200

12800

14400

16000

tp

column

Moment ( kip-inch )


0.4

1.2

cc

pc

li

pt

ct

1.6

2.0

2.4

2.8

3.2


gc


0.8

beam

gt

3.6

lp

4.0

nc

ni

nt

A.5 – 133


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2976E+05 0.2693E+04 0.1969E+05 2 0.02 580.35 52.51 513.73 0.2976E+05 0.2693E+04 0.2961E+05 3 0.04 1160.70 105.02 1115.74 0.2792E+05 0.2693E+04 0.3145E+05 4 0.06 1741.15 165.61 1811.95 0.2580E+05 0.2693E+04 0.3004E+05 5 0.08 2321.60 226.21 2457.12 0.2933E+05 0.2694E+04 0.2719E+05 6 0.10 2935.64 277.39 2948.59 0.3232E+05 0.2694E+04 0.2455E+05 7 0.12 3549.68 328.58 3390.90 0.2686E+05 0.2695E+04 0.2205E+05 8 0.16 4144.01 425.59 4110.57 0.1651E+05 0.2696E+04 0.1812E+05 9 0.19 4738.33 522.65 4709.22 0.1466E+05 0.2698E+04 0.1531E+05 10 0.25 5366.75 664.29 5438.64 0.1197E+05 0.2701E+04 0.1273E+05 11 0.30 5995.16 806.10 6065.17 0.1184E+05 0.2705E+04 0.1127E+05 12 0.35 6610.06 948.12 6632.37 0.1171E+05 0.2710E+04 0.1040E+05 13 0.40 7224.96 1090.38 7161.41 0.1052E+05 0.2715E+04 0.9782E+04 14 0.47 7820.03 1269.59 7785.12 0.9016E+04 0.2723E+04 0.9127E+04 15 0.54 8415.11 1449.33 8366.31 0.8061E+04 0.2733E+04 0.8481E+04 16 0.59 8816.60 1600.45 8819.80 0.7254E+04 0.2742E+04 0.7917E+04 17 0.65 9218.09 1752.33 9242.41 0.7254E+04 0.2751E+04 0.7338E+04 18 0.70 9619.58 1904.47 9632.16 0.6661E+04 0.2762E+04 0.6759E+04 19 0.77 10039.47 2103.85 10088.07 0.5885E+04 0.2777E+04 0.6036E+04 20 0.84 10459.36 2302.16 10494.68 0.5885E+04 0.2794E+04 0.5364E+04 21 0.92 10879.25 2501.40 10855.23 0.5331E+04 0.2813E+04 0.4762E+04 22 1.05 11440.01 2870.83 11413.25 0.3920E+04 0.2852E+04 0.3866E+04 23 1.18 11904.17 3246.73 11877.11 0.3141E+04 0.2898E+04 0.3212E+04 24 1.31 12271.74 3639.80 12273.55 0.2658E+04 0.2952E+04 0.2763E+04 25 1.45 12619.13 4040.69 12627.19 0.2465E+04 0.3015E+04 0.2468E+04 26 1.58 12946.36 4465.96 12953.92 0.2371E+04 0.3089E+04 0.2283E+04 --------------------------------------------------------------------------------------------------




A.5 – 134



1) 2)

li pi gc ni

= 18.3100" = 11.5600" = 6.5000" = 2 X 2 nc = 2 X

3

5.4700" 3.3750"

------------------------------




Remark




Major parameters

U.S.A

: :

A.Mazroi (1983) EP8 With Shim

Tested by Test Id.

V - 68

0 0.0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

tp

column

Moment ( kip-inch )


0.6

1.8

cc

pc

li

pt

ct

2.4

3.0

3.6

4.2

4.8


gc


1.2

beam

gt

5.4

lp

6.0

nc

ni

nt

A.5 – 135


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.25783333E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.35662055E+05 -0.21193927E+06 0.63736748E+06 -0.10139707E+07 0.79208594E+06 Rj0 = 0.0000 0.2000 RKj = 0.44030936E+05 -0.43071183E+05



A.5 – 136


: :


1) 2)

li pi gc ni

= 19.7500" = 14.5000" = 5.5000" = 2 X 2 3

3.5000" 2.6250"

nc = 2 X

pc = pic=


End plate was stiffened in the plane of beam web by an end-plate. pic=poc and pit=pot

End plate extended on both sides. ct = 4.1250" pt = 3.5000" cc = 4.1250" pit= 2.6250" gt = 5.5000" gi = 5.5000" tp = 1.0000" nt = 2 X 3

Remark

U.S.A Fasteners: A325- -7/8"D 15/16" Oversize holes Material : A36 Fy = 46.80 ksi Fu = -ksi

Major parameters

A.Mazroi (1984) CF4-U12x87


Tested by Test Id.

V - 69

0

850

1700

2550

3400

4250

5100

5950

6800

7650

8500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

li

pt

ct

8

10

12

14

16


gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 137


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 138


: :

© 2011 J. Ross Publishing, Inc. li pi gc ni

= 19.7500" = 14.5000" = 5.5000" = 2 X 2 3

3.5000" 2.6250"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V - 70

0

1250

2500

3750

5000

6250

7500

8750

10000

11250

12500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

li

pt

ct

8

10

12

14

16


gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 139


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 140


: :


= 19.7500" = 14.5000" = 5.5000" = 2 X 2 3

3.5000" 2.6250"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V - 71

0 0.0

1200

2400

3600

4800

6000

7200

8400

9600

10800

12000

tp

column

Moment ( kip-inch )


0.7

2.1

cc

pc

li

pt

ct

2.8

3.5

4.2

4.9

5.6


gc


1.4

beam

gt

6.3

lp

7.0

nc

ni

nt

A.5 – 141


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 142


: :


= 22.3901" = 17.0567" = 5.5000" = 2 X 2 3

3.9300" 2.6667"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark

U.S.A Fasteners: A325- -1"D 1 1/16" Oversize holes Material : A36 Fy = 40.60 ksi Fu = -ksi

Major parameters



Tested by Test Id.

V - 72

0 0.0

900

1800

2700

3600

4500

5400

6300

7200

8100

9000

tp

column

Moment ( kip-inch )


0.8

2.4

3.2

4.0

4.8

5.6

cc

pc

li

pt

ct

6.4


gc


1.6

beam

gt

7.2

lp

8.0

nc

ni

nt

A.5 – 143


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 144


: :


= 22.3901" = 17.0567" = 5.5000" = 2 X 2 3

3.9300" 2.6667"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V - 73

0 0.0

650

1300

1950

2600

3250

3900

4550

5200

5850

6500

tp

column

Moment ( kip-inch )


0.9

2.7

3.6

4.5

5.4

6.3

cc

pc

li

pt

ct

7.2


gc


1.8

beam

gt

8.1

lp

9.0

nc

ni

nt

A.5 – 145


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 146


: :


= 22.3901" = 17.0567" = 5.5000" = 2 X 2 3

3.9300" 2.6667"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V - 74

0 0.0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0.7

2.1

2.8

3.5

4.2

4.9

cc

pc

li

pt

ct

5.6


gc


1.4

beam

gt

6.3

lp

7.0

nc

ni

nt

A.5 – 147


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 148


: :


= 21.3900" = 15.3900" = 6.5000" = 2 X 2 3

4.9300" 3.0000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V - 75

0 0.0

900

1800

2700

3600

4500

5400

6300

7200

8100

9000

tp

column

Moment ( kip-inch )


0.7

2.1

2.8

3.5

4.2

4.9

cc

pc

li

pt

ct

5.6


gc


1.4

beam

gt

6.3

lp

7.0

nc

ni

nt

A.5 – 149


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 150


: :


= 21.3900" = 15.3900" = 6.5000" = 2 X 2 3

4.9300" 3.0000"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark


Major parameters



Tested by Test Id.

V - 76

0

1450

2900

4350

5800

7250

8700

10150

11600

13050

14500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

li

pt

ct

8

10

12

14

16


gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 151


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 152


: :


= 18.3100" = 11.5600" = 6.5000" = 2 X 2 3

5.4700" 3.3750"

nc = 2 X

pc = pic=

------------------------------




1) 2)


Remark

U.S.A Fasteners: A325- -1 1/8"D 1 1/4" Oversize holes Material : A36 Fy = 35.00 ksi Fu = -ksi

Major parameters



Tested by Test Id.

V - 77

0

1750

3500

5250

7000

8750

10500

12250

14000

15750

17500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

li

pt

ct

8

10

12

14

16


gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 153


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 154



1) 2)

li pi gc ni

= 19.7500" = 14.5000" = 5.5000" = 2 X 2

------------------------------


3

3.5000" 2.6250"

nc = 2 X

End plate was stiffened in the plane of beam web. pic=poc and pit=pot


Remark



Column : W12x65 Beam : W24x100 Plate thickness : 3/4" Stiffener thickness : 0.3750"

Major parameters

U.S.A

: :

A.Mazroi (1983) CF3-S12x65

Tested by Test Id.

V - 78

0 0.0

750

1500

2250

3000

3750

4500

5250

6000

6750

7500

tp

column

Moment ( kip-inch )


0.5

1.5

2.0

2.5

3.0

3.5

cc

pc

li

pt

ct

4.0


gc


1.0

beam

gt

4.5

lp

5.0

nc

ni

nt

A.5 – 155


A3 = P3 =

2.040000 5

K = Q1 =

0.000446 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 156



1) 2)

li pi gc ni

= 19.7500" = 14.5000" = 5.5000" = 2 X 2

------------------------------


3

3.5000" 2.6250"

nc = 2 X

End plate was stiffened in the plane of beam web. pic=poc and pit=pot


Remark



Column : W12x87 Beam : W24x100 Plate thickness : 1" Stiffener thickness : 0.3750"

Major parameters

U.S.A

: :


Tested by Test Id.

V - 79

0 0.0

1200

2400

3600

4800

6000

7200

8400

9600

10800

12000

tp

column

Moment ( kip-inch )


0.6

1.8

cc

pc

li

pt

ct

2.4

3.0

3.6

4.2

4.8


gc


1.2

beam

gt

5.4

lp

6.0

nc

ni

nt

A.5 – 157


A3 = P3 =

2.040000 5

K = Q1 =

0.000375 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 158



1) 2)

li pi gc ni

= 22.3901" = 17.0567" = 5.5000" = 2 X 2 nc = 2 X

3

3.9300" 2.6667"

------------------------------




Remark




Major parameters

U.S.A

: :


Tested by Test Id.

V - 80

0 0.0

850

1700

2550

3400

4250

5100

5950

6800

7650

8500

tp

column

Moment ( kip-inch )


0.4

1.2

1.6

2.0

2.4

2.8

cc

pc

li

pt

ct

3.2


gc


0.8

beam

gt

3.6

lp

4.0

nc

ni

nt

A.5 – 159


A3 = P3 =

2.040000 5

K = Q1 =

0.000279 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.13000000E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.47667464E+04 0.76513777E+05 -0.35453545E+06 0.74008136E+06 -0.71934246E+06 Rj0 = 0.0400 0.9900 RKj = 0.31078137E+04 -0.18242942E+04



A.5 – 160



1) 2)

li pi gc ni

= 22.3901" = 17.0567" = 5.5000" = 2 X 2 nc = 2 X

3

3.9300" 2.6667"

------------------------------




Remark




Major parameters

U.S.A

: :


Tested by Test Id.

V - 81

0 0.0

1450

2900

4350

5800

7250

8700

10150

11600

13050

14500

tp

column

Moment ( kip-inch )


0.6

1.8

cc

pc

li

pt

ct

2.4

3.0

3.6

4.2

4.8


gc


1.2

beam

gt

5.4

lp

6.0

nc

ni

nt

A.5 – 161


A3 = P3 =

2.040000 5

K = Q1 =

0.000279 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 162



1) 2)

li pi gc ni

= 21.3900" = 15.3900" = 6.5000" = 2 X 2 nc = 2 X

3

4.9300" 3.0000"

------------------------------




Remark



Column : W12x79 Beam : W27x114 Plate thickness : 1 1/4" Stiffener thickness : 0.3750"

Major parameters

U.S.A

: :


Tested by Test Id.

V - 82

0 0.0

1050

2100

3150

4200

5250

6300

7350

8400

9450

10500

tp

column

Moment ( kip-inch )


0.7

2.1

cc

pc

li

pt

ct

2.8

3.5

4.2

4.9

5.6


gc


1.4

beam

gt

6.3

lp

7.0

nc

ni

nt

A.5 – 163


A3 = P3 =

2.040000 5

K = Q1 =

0.000226 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.45191667E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.45222545E+04 -0.21031166E+05 0.47298017E+05 -0.32944240E+05 -0.17497345E+05 Rj0 = 0.0000 RKj = 0.45813126E+03



A.5 – 164



1) 2)

li pi gc ni

= 18.3100" = 11.5600" = 6.5000" = 2 X 2 nc = 2 X

3

5.4700" 3.3750"

------------------------------




Remark




Major parameters

U.S.A

: :


Tested by Test Id.

V - 83

0 0.0

1750

3500

5250

7000

8750

10500

12250

14000

15750

17500

tp

column

Moment ( kip-inch )


0.8

2.4

cc

pc

li

pt

ct

3.2

4.0

4.8

5.6

6.4


gc


1.6

beam

gt

7.2

lp

8.0

nc

ni

nt

A.5 – 165


A3 = P3 =

2.040000 5

K = Q1 =

0.000217 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 166



1) 2)

li pi gc ni

= 18.3100" = 11.5600" = 6.5000" = 2 X 2 nc = 2 X

3

5.4700" 3.3750"

------------------------------




Remark




Major parameters

U.S.A

: :


Tested by Test Id.

V - 84

0 0.0

1850

3700

5550

7400

9250

11100

12950

14800

16650

18500

tp

column

Moment ( kip-inch )


0.6

1.8

cc

pc

li

pt

ct

2.4

3.0

3.6

4.2

4.8


gc


1.2

beam

gt

5.4

lp

6.0

nc

ni

nt

A.5 – 167


A3 = P3 =

2.040000 5

K = Q1 =

0.000217 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 168


: :

Y.L.Yee (1984) K1B


7.5866"

------------------------------


32 mm Doubler plates were welded to flange on both sides of column web. End-plate yield stress (Fy) is mentioned.


1) 2)


Remark

Australia Fasteners: G8.8- -M30 1 1/4" Oversize holes Material : G250 Fy = 37.70 ksi Fu = -ksi

Major parameters

Column : 460UB67.1 Beam : 460UB67.1 Plate thickness : 32 mm Stiffener thickness : 0.6299"

Tested by Test Id.

V - 85

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

li

pt

ct

16

20

24

28

32

Material : G250 Fy = 37.70 ksi : Experimental : Polynominal : M. Exponential

gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 169


A3 = P3 =

2.040000 5

K = Q1 =

0.000490 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 170


: :

Y.L.Yee (1984) K9


7.5866"

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 86

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

li

pt

ct

16

20

24

28

32


gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 171


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 172


: :

Y.L.Yee (1984) K4


7.5866"

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 87

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

li

pt

ct

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.5 – 173


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7149E+03 0.8603E+03 0.6412E+03 3 0.55 290.28 470.11 314.88 0.5072E+03 0.8333E+03 0.5176E+03 5 1.12 617.60 916.03 595.62 0.5032E+03 0.7317E+03 0.4807E+03 7 1.74 878.42 1319.74 884.99 0.4274E+03 0.5645E+03 0.4494E+03 9 2.43 1179.74 1653.03 1182.99 0.4363E+03 0.4104E+03 0.4137E+03 11 3.20 1485.37 1924.76 1488.52 0.3621E+03 0.3017E+03 0.3773E+03 13 4.06 1795.32 2149.73 1795.88 0.3535E+03 0.2301E+03 0.3414E+03 15 4.88 2078.86 2319.67 2062.60 0.3103E+03 0.1869E+03 0.3084E+03 17 6.05 2390.39 2513.19 2395.12 0.2649E+03 0.1476E+03 0.2608E+03 19 7.25 2674.87 2674.36 2679.77 0.2137E+03 0.1216E+03 0.2119E+03 21 8.51 2907.60 2814.37 2915.19 0.1553E+03 0.1031E+03 0.1651E+03 23 9.47 3056.92 2908.96 3059.71 0.1527E+03 0.9242E+02 0.1338E+03 25 10.55 3195.37 3002.73 3187.03 0.1111E+03 0.8305E+02 0.1050E+03 27 11.81 3306.73 3101.70 3302.05 0.6752E+02 0.7432E+02 0.7882E+02 29 13.12 3395.59 3194.57 3392.11 0.4805E+02 0.6709E+02 0.5922E+02 31 14.47 3433.48 3280.90 3462.13 0.4708E+02 0.6110E+02 0.4553E+02 33 16.51 3552.11 3398.09 3540.44 -0.1478E+03 0.5395E+02 -0.1686E+03 35 17.27 3521.88 3438.46 3521.87 0.7413E+02 0.5172E+02 0.7303E+02 --------------------------------------------------------------------------------------------------




A.5 – 174


: :

Y.L.Yee (1984) K7


7.5866"

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 88

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

li

pt

ct

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.5 – 175


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 176


: :

Y.L.Yee (1984) K5A


7.5866"

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 89

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

li

pt

ct

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.5 – 177


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 178


: :

Y.L.Yee (1984) K8


7.5866"

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 90

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

li

pt

ct

16

20

24

28

32


gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 179


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 180


: :

Y.L.Yee (1984) K10


7.5866"

------------------------------




1) 2)


Remark


Major parameters


Tested by Test Id.

V - 91

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 181


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.8109E+03 0.8603E+03 0.9153E+03 3 0.36 294.36 310.98 300.03 0.8400E+03 0.8493E+03 0.7309E+03 5 0.71 593.67 598.64 525.74 0.7308E+03 0.8135E+03 0.5843E+03 7 1.95 889.36 1434.09 1054.08 -0.2100E+04 0.5107E+03 0.3211E+03 9 2.08 1195.83 1498.04 1094.74 0.5430E+03 0.4808E+03 0.3096E+03 11 3.17 1498.76 1915.89 1402.04 0.5283E+03 0.3049E+03 0.2644E+03 13 4.78 1782.54 2301.68 1813.84 0.1889E+03 0.1911E+03 0.2478E+03 15 6.11 2100.74 2522.14 2128.47 0.2985E+03 0.1460E+03 0.2248E+03 17 7.00 2373.50 2643.63 2320.46 0.3427E+03 0.1262E+03 0.2031E+03 19 9.04 2680.34 2868.34 2679.66 0.1866E+03 0.9686E+02 0.1493E+03 21 10.82 2946.65 3025.09 2907.38 0.1018E+03 0.8098E+02 0.1092E+03 23 13.85 3148.38 3242.39 3163.04 0.6150E+02 0.6369E+02 0.6387E+02 25 16.74 3294.41 3410.19 3311.15 0.4311E+02 0.5327E+02 0.4120E+02 27 19.88 3407.84 3564.49 3418.59 0.2869E+02 0.4543E+02 0.2864E+02 29 22.93 3495.40 3694.27 3495.41 0.2563E+02 0.3988E+02 0.2235E+02 31 26.38 3571.93 3823.38 3565.39 0.2217E+02 0.3516E+02 0.1861E+02 33 29.60 3632.97 3930.72 3621.97 0.1528E+02 0.3173E+02 0.1676E+02 35 32.58 3678.51 4022.25 3670.35 0.1528E+02 0.2913E+02 0.1580E+02 37 35.54 3715.09 4105.03 3716.20 0.9416E+01 0.2699E+02 0.1526E+02 39 38.47 3742.71 4181.45 3760.47 0.9416E+01 0.2519E+02 0.1495E+02 --------------------------------------------------------------------------------------------------




A.5 – 182


: :

Y.L.Yee (1984) K11


7.5866"

------------------------------


The beam, 3 deg. to horizontal was subjected to cantilever loading. End-plate yield stress (Fy) is mentioned.


1) 2)


Remark


Major parameters


Tested by Test Id.

V - 92

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 183


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 184


: :


7.5866"

------------------------------




1) 2)


Remark


Major parameters

Y.L.Yee (1984) K12

Column : 460UB67.1 Beam : 460UB67.1 Plate thickness : 20 mm

Tested by Test Id.

V - 93

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 185


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 186


: :

Y.L.Yee (1984) B1


7.5866"

------------------------------


The beam stub, 3 deg. to horizontal was subjected to cantilever loading. End-plate yield stress (Fy) is mentioned.


1) 2)


Remark


Major parameters

Column : 310UC96.8 Beam : 460UB67.1 Plate thickness : 20 mm Stiffener thickness : 0.4724"

Tested by Test Id.

V - 94

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 187


A3 = P3 =

2.040000 5

K = Q1 =

0.000649 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 188


: :


7.5866"

------------------------------




1) 2)


Remark


Major parameters

Y.L.Yee (1984) B2

Column : 310UC96.8 Beam : 460UB67.1 Plate thickness : 20 mm

Tested by Test Id.

V - 95

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

li

pt

ct

20

25

30

35

40


gc


10

beam

gt

45

lp

50

nc

ni

nt

A.5 – 189


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 190


: :


7.5866"

------------------------------




1) 2)


Remark


Major parameters

Y.L.Yee (1984) B3

Column : 310UC96.8 Beam : 460UB67.1 Plate thickness : 16 mm

Tested by Test Id.

V - 96

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 191


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 192


: :

Y.L.Yee (1984) C1


5.7165"

------------------------------




1) 2)


Remark

Australia Fasteners: G8.8- -M20 13/16" Oversize holes Material : G250 Fy = 36.69 ksi Fu = -ksi

Major parameters


Tested by Test Id.

V - 97

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

li

pt

ct

20

25

30

35

40


gc


10

beam

gt

45

lp

50

nc

ni

nt

A.5 – 193


A3 = P3 =

2.040000 5

K = Q1 =

0.001602 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 194


: :


5.7165"

------------------------------




1) 2)


Remark


Major parameters

Y.L.Yee (1984) C2


Tested by Test Id.

V - 98

0

90

180

270

360

450

540

630

720

810

900

tp

column

Moment ( kip-inch )


0

6

18

24

30

36

42

cc

pc

li

pt

ct

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 195


A3 = P3 =

2.040000 5

K = Q1 =

0.002428 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7370E+02 0.2301E+03 -0.5917E+02 3 0.67 49.09 150.92 48.29 0.7370E+02 0.2191E+03 0.8208E+02 5 1.30 108.82 279.54 108.16 0.1171E+03 0.1830E+03 0.1066E+03 7 1.90 179.19 376.39 177.86 0.1171E+03 0.1399E+03 0.1241E+03 9 2.43 245.28 441.71 245.81 0.1369E+03 0.1099E+03 0.1333E+03 11 2.88 307.10 486.85 307.04 0.1369E+03 0.9109E+02 0.1375E+03 13 4.70 371.40 610.92 371.48 0.2097E+02 0.5217E+02 0.2105E+02 15 7.88 438.17 734.79 437.73 0.2097E+02 0.2982E+02 0.2149E+02 17 11.06 504.95 814.24 506.87 0.2097E+02 0.2118E+02 0.2095E+02 19 14.25 571.73 873.70 565.80 0.1540E+02 0.1658E+02 0.1563E+02 21 17.40 602.91 921.20 606.05 0.9887E+01 0.1374E+02 0.1017E+02 23 20.56 634.10 961.27 632.42 0.8008E+01 0.1178E+02 0.6953E+01 25 24.27 655.63 1001.83 655.44 0.5793E+01 0.1013E+02 0.5805E+01 27 27.99 677.16 1037.13 677.40 0.5793E+01 0.8918E+01 0.6151E+01 29 31.53 691.76 1067.06 691.69 0.2277E+01 0.8024E+01 0.1676E+01 31 34.89 699.42 1092.86 698.46 0.2277E+01 0.7340E+01 0.2324E+01 33 38.26 707.08 1116.56 707.14 0.2277E+01 0.6773E+01 0.2813E+01 --------------------------------------------------------------------------------------------------




A.5 – 196


: :


6.4094"

------------------------------




1) 2)


Remark


Major parameters

Y.L.Yee (1984) D1


Tested by Test Id.

V - 99

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 197


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 198


: :


6.4094"

------------------------------




1) 2)


Remark


Major parameters

Y.L.Yee (1984) D2


Tested by Test Id.

V -100

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

li

pt

ct

20

25

30

35

40


gc


10

beam

gt

45

lp

50

nc

ni

nt

A.5 – 199


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 200


: :



1.6142"

------------------------------


Slip occurred at a relatively high moment


1) 2)


Remark

United Kingdom

Fasteners: G8.8- -M16 23/32" Oversize holes Material : 43A Fy = -ksi Fu = -ksi

J.B.Davison et al. (1987) JT/13B

Column : UC 152x152x23 Beam : UB 254x102x22 Plate thickness : 15 mm

Tested by Test Id.

V -101

0

65

130

195

260

325

390

455

520

585

650

tp

column

Moment ( kip-inch )


0

2

6

8

12

14

cc

pc

pic

pi pi

pit

pt

ct

16

: 43A Experimental Polynominal M. Exponential

10

Material : : :


4

beam

gt

18

li

20

nc

ni

nt

A.5 – 201


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.5752E+02 0.5879E+02 0.3751E+02 2 0.38 22.12 22.67 28.40 0.7031E+02 0.5924E+02 0.6453E+02 3 0.58 36.87 34.11 41.70 0.1467E+05 0.5980E+02 0.7437E+02 4 0.58 51.62 34.11 41.70 0.1470E+05 0.5980E+02 0.7437E+02 5 0.87 73.75 51.54 65.12 0.6519E+02 0.6113E+02 0.8649E+02 6 1.35 95.87 81.72 107.92 0.6794E+02 0.6479E+02 0.8891E+02 7 1.54 110.62 94.38 124.87 0.1340E+03 0.6687E+02 0.8736E+02 8 1.73 147.49 107.50 141.57 0.1532E+03 0.6940E+02 0.8611E+02 9 1.92 169.62 121.10 158.05 0.9599E+02 0.7241E+02 0.8571E+02 10 2.12 184.37 135.35 174.56 0.7353E+02 0.7597E+02 0.8625E+02 11 2.69 221.24 183.01 225.69 0.7363E+02 0.9008E+02 0.9150E+02 12 2.88 235.99 200.82 243.43 0.9579E+02 0.9519E+02 0.9333E+02 13 3.08 258.11 219.59 261.55 0.1661E+03 0.9926E+02 0.9468E+02 14 3.17 276.55 229.14 270.68 0.1715E+03 0.1004E+03 0.9511E+02 15 3.61 311.58 272.06 311.83 0.8096E+02 0.9443E+02 0.9437E+02 16 4.04 346.61 309.02 351.65 0.9375E+02 0.7538E+02 0.8895E+02 17 4.33 376.10 328.92 376.49 0.1023E+03 0.6326E+02 0.8300E+02 18 4.62 405.60 345.71 399.40 0.8947E+02 0.5354E+02 0.7561E+02 19 5.19 442.48 372.52 438.14 0.4858E+02 0.4022E+02 0.5833E+02 20 5.58 457.23 386.74 458.26 0.3579E+02 0.3443E+02 0.4638E+02 21 6.15 475.66 404.73 480.14 0.3196E+02 0.2829E+02 0.2991E+02 22 6.73 494.10 419.75 493.43 0.2100E+02 0.2406E+02 0.1681E+02 23 7.40 499.63 434.69 501.05 0.8218E+01 0.2054E+02 0.6818E+01 24 8.08 505.16 447.61 503.87 0.5501E+01 0.1797E+02 0.2432E+01 25 8.85 507.00 460.54 505.67 0.2396E+01 0.1577E+02 0.3105E+01 26 9.62 508.85 471.99 509.75 -0.1358E+02 0.1408E+02 0.8065E+01 27 10.19 494.10 479.81 494.10 -0.2557E+02 0.1305E+02 -0.2465E+02 --------------------------------------------------------------------------------------------------




A.5 – 202


: :



2.7166"

------------------------------


Faiulre of column flange at 221.24 lb in Web flange fracture followed by bolt failure at 677 lb in


1) 2)


Remark

United Kingdom


D.B.Moore & P.A.C.Sims (1986) J3


Tested by Test Id.

V -102

0

85

170

255

340

425

510

595

680

765

850

tp

column

Moment ( kip-inch )


0

11

33

44

66

77

cc

pc

pic

pi pi

pit

pt

ct

88


55

Material : : :


22

beam

gt

99

li

110

nc

ni

nt

A.5 – 203


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 204


: :



2.7166"

------------------------------


Tested with backing plates


1) 2)


Remark

United Kingdom


D.B.Moore & P.A.C.Sims (1986) J4


Tested by Test Id.

V -103

0

85

170

255

340

425

510

595

680

765

850

tp

column

Moment ( kip-inch )


0

6

18

24

36

42

cc

pc

pic

pi pi

pit

pt

ct

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 205


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 206


: :



2.3622"

------------------------------


The specimen was connected to a counter beam with negligible deformation End-plate extended on both tension & compression sides


1) 2)


Remark

Italy


R.Zandonini & P.Zanon (1987) EP 1-1

Column : ---Beam : IPE 300 Plate thickness : 12 mm

Tested by Test Id.

V -104

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

14

42

56

84

98

cc

pc

pic

pi pi

pit

pt

ct

li

nc

ni

nt

112 126 140


70

Material : : :


28

beam

gt

A.5 – 207


A3 = P3 =

2.040000 5

K = Q1 =

0.004187 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2656E+03 0.1334E+03 0.3441E+03 3 0.48 148.73 63.56 152.80 0.3437E+03 0.1303E+03 0.2933E+03 5 0.98 297.46 126.17 287.43 0.2493E+03 0.1184E+03 0.2462E+03 7 1.76 446.20 206.52 454.87 0.1779E+03 0.8668E+02 0.1857E+03 9 2.68 594.93 271.49 599.94 0.1566E+03 0.5719E+02 0.1328E+03 11 3.70 743.66 319.91 713.80 0.1027E+03 0.3966E+02 0.9336E+02 13 5.74 840.34 382.56 856.85 0.4328E+02 0.2422E+02 0.5347E+02 15 8.46 966.76 435.86 974.66 0.4701E+02 0.1607E+02 0.3650E+02 17 12.20 1115.49 485.46 1093.03 0.3005E+02 0.1117E+02 0.2753E+02 19 18.70 1219.60 544.24 1228.05 0.1220E+02 0.7454E+01 0.1482E+02 21 24.39 1293.97 581.70 1295.46 0.1250E+02 0.5850E+01 0.9891E+01 23 32.52 1368.33 623.38 1370.66 0.9147E+01 0.4529E+01 0.9093E+01 25 40.65 1442.70 656.70 1442.82 0.8461E+01 0.3726E+01 0.8405E+01 27 45.53 1487.32 673.99 1481.32 0.7187E+01 0.3378E+01 0.7318E+01 29 52.84 1524.50 697.15 1527.64 0.5488E+01 0.2972E+01 0.5327E+01 31 60.98 1561.69 719.87 1562.58 0.3659E+01 0.2631E+01 0.3357E+01 33 69.11 1579.54 740.13 1583.85 0.7318E+00 0.2366E+01 0.1976E+01 35 77.23 1594.41 758.47 1596.18 0.2927E+01 0.2154E+01 0.1134E+01 37 85.36 1606.31 775.26 1603.29 0.5043E-03 0.1980E+01 0.6642E+00 --------------------------------------------------------------------------------------------------




A.5 – 208


: :



2.3622"

------------------------------


The specimen was connected to a counter beam with negligible deformability End-plate extended on tension side only


1) 2)


Remark

Italy



Column : --Beam : IPE 300 Plate thickness : 15 mm

Tested by Test Id.

V -105

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

10

30

40

60

70

cc

pc

pic

pi pi

pit

pt

ct

80


50

Material : : :


20

beam

gt

90

li

100

nc

ni

nt

A.5 – 209


A3 = P3 =

2.040000 5

K = Q1 =

0.003662 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.5795E+03 0.1525E+03 0.7647E+03 3 0.29 162.25 44.12 162.14 0.5245E+03 0.1513E+03 0.5198E+03 5 0.62 324.51 93.36 318.36 0.4643E+03 0.1464E+03 0.4268E+03 7 0.99 486.76 145.61 487.17 0.4166E+03 0.1350E+03 0.4913E+03 9 1.40 649.01 197.31 667.27 0.3737E+03 0.1165E+03 0.3896E+03 11 1.86 811.27 245.70 823.31 0.3468E+03 0.9461E+02 0.2935E+03 13 2.35 966.76 286.90 945.70 0.2922E+03 0.7552E+02 0.2128E+03 15 3.27 1085.74 344.77 1090.67 0.6613E+02 0.5227E+02 0.1121E+03 17 4.88 1189.86 411.33 1201.71 0.5421E+02 0.3314E+02 0.4154E+02 19 8.13 1308.84 492.09 1299.54 0.3202E+02 0.1915E+02 0.2765E+02 21 11.38 1398.10 544.32 1385.39 0.2135E+02 0.1366E+02 0.2386E+02 23 16.26 1457.57 600.12 1478.62 0.1585E+02 0.9705E+01 0.1550E+02 25 20.32 1561.69 635.60 1537.34 0.1785E+02 0.7894E+01 0.1393E+02 27 24.39 1591.43 665.09 1593.20 0.1087E+02 0.6689E+01 0.1345E+02 29 27.64 1636.05 685.64 1635.21 0.1262E+02 0.5980E+01 0.1224E+02 31 32.52 1689.60 712.75 1687.87 0.9146E+01 0.5178E+01 0.9182E+01 33 37.40 1725.29 736.50 1724.34 0.4023E+01 0.4581E+01 0.5813E+01 35 40.65 1731.24 750.85 1739.99 0.3619E+01 0.4260E+01 0.3875E+01 37 44.72 1755.04 767.63 1751.67 0.3659E+01 0.3920E+01 0.1973E+01 39 48.78 1760.99 782.96 1756.79 -0.2616E+00 0.3637E+01 0.6275E+00 41 54.20 1747.10 801.67 1746.49 -0.2562E+01 0.3325E+01 -0.4317E+01 43 58.95 1725.29 816.98 1724.58 -0.7307E+01 0.3094E+01 -0.4869E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.54316667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.13155022E+04 0.21109539E+05 -0.87033819E+05 0.18152881E+06 -0.18190643E+06 Rj0 = 0.0000 0.8100 51.4900 RKj = -0.16763051E+03 0.16592072E+03 -0.38258506E+01



A.5 – 210


: :



2.3622"

------------------------------




1) 2)


Remark

Italy




Tested by Test Id.

V -106

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

6

18

24

cc

pc

pic

pi pi

pit

pt

ct

36

42

48


30

Material : : :


12

beam

gt

54

li

60

nc

ni

nt

A.5 – 211


A3 = P3 =

2.040000 5

K = Q1 =

0.003283 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 212


: :



2.3622"

------------------------------




1) 2)


Remark

Italy




Tested by Test Id.

V -107

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

5

15

20

cc

pc

pic

pi pi

pit

pt

ct

30

35

40


25

Material : : :


10

beam

gt

45

li

50

nc

ni

nt

A.5 – 213


A3 = P3 =

2.040000 5

K = Q1 =

0.002911 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2366E+04 0.1919E+03 0.1766E+04 3 0.10 189.30 19.19 160.28 0.1408E+04 0.1918E+03 0.1452E+04 5 0.28 378.59 53.61 382.50 0.8748E+03 0.1905E+03 0.1046E+04 7 0.54 567.89 102.66 604.88 0.1307E+04 0.1862E+03 0.7009E+03 9 0.78 757.18 146.54 750.52 0.5009E+03 0.1790E+03 0.5295E+03 11 1.20 946.48 217.74 938.78 0.4131E+03 0.1586E+03 0.3886E+03 13 1.70 1115.49 289.49 1112.64 0.2762E+03 0.1283E+03 0.3143E+03 15 2.28 1264.22 354.63 1276.78 0.2404E+03 0.9788E+02 0.2528E+03 17 2.94 1412.95 410.85 1421.91 0.2128E+03 0.7420E+02 0.1879E+03 19 3.68 1561.69 459.06 1537.41 0.1465E+03 0.5742E+02 0.1270E+03 21 4.88 1636.05 517.51 1648.74 0.5031E+02 0.4171E+02 0.6647E+02 23 6.50 1725.29 575.17 1728.20 0.4574E+02 0.3046E+02 0.3806E+02 25 8.13 1784.78 619.10 1784.02 0.3659E+02 0.2410E+02 0.3190E+02 27 9.76 1844.28 654.75 1832.95 0.2927E+02 0.2002E+02 0.2809E+02 29 12.20 1888.90 698.38 1891.99 0.1830E+02 0.1607E+02 0.2001E+02 31 14.63 1933.52 734.22 1930.79 0.9512E+01 0.1349E+02 0.1212E+02 33 16.26 1939.46 755.08 1947.12 0.5365E+01 0.1221E+02 0.8161E+01 35 18.70 1958.80 782.96 1961.81 0.7928E+01 0.1072E+02 0.4245E+01 37 21.14 1978.14 807.67 1969.27 0.2805E+01 0.9582E+01 0.2104E+01 39 23.93 1969.64 832.90 1968.67 -0.3049E+01 0.8564E+01 -0.2375E+01 41 26.71 1961.14 855.61 1961.21 -0.3049E+01 0.7757E+01 -0.2901E+01 43 29.50 1952.64 876.29 1952.77 -0.3049E+01 0.7101E+01 -0.3125E+01 --------------------------------------------------------------------------------------------------




A.5 – 214


: :



2.3622"

------------------------------




1) 2)


Remark

Italy




Tested by Test Id.

V -108

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

5

15

20

cc

pc

pic

pi pi

pit

pt

ct

30

35

40


25

Material : : :


10

beam

gt

45

li

50

nc

ni

nt

A.5 – 215


A3 = P3 =

2.040000 5

K = Q1 =

0.002695 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3144E+04 0.2073E+03 0.1551E+04 3 0.07 189.30 14.55 194.29 0.2151E+04 0.2072E+03 0.2510E+04 5 0.18 378.59 37.37 377.08 0.1471E+04 0.2066E+03 0.1297E+04 7 0.33 567.89 68.26 557.61 0.1121E+04 0.2051E+03 0.1111E+04 9 0.52 757.18 106.96 748.92 0.9046E+03 0.2015E+03 0.9060E+03 11 0.85 946.48 171.83 999.54 0.9811E+03 0.1902E+03 0.6277E+03 13 1.06 1115.49 211.09 1118.10 0.5439E+03 0.1794E+03 0.4951E+03 15 1.36 1264.22 260.98 1241.97 0.4160E+03 0.1612E+03 0.3600E+03 17 2.03 1412.95 355.27 1419.46 0.1829E+03 0.1185E+03 0.1902E+03 19 3.25 1561.69 467.21 1582.40 0.1896E+03 0.7144E+02 0.9974E+02 21 5.04 1710.42 565.94 1720.53 0.5081E+02 0.4343E+02 0.5839E+02 23 7.32 1814.53 646.16 1814.38 0.3659E+02 0.2903E+02 0.2851E+02 25 9.35 1866.59 698.03 1862.62 0.1829E+02 0.2256E+02 0.2096E+02 27 11.79 1911.21 746.96 1911.32 0.1829E+02 0.1793E+02 0.1909E+02 29 14.09 1948.39 784.78 1951.93 0.1373E+02 0.1510E+02 0.1576E+02 31 16.26 1978.14 815.32 1981.11 0.1061E+02 0.1319E+02 0.1105E+02 33 18.86 1995.99 847.31 2002.37 0.6860E+01 0.1149E+02 0.5449E+01 35 21.46 2013.84 875.45 2010.68 0.6860E+01 0.1020E+02 0.1202E+01 37 23.58 2019.79 896.23 2010.60 -0.3659E+01 0.9366E+01 -0.1122E+01 39 25.69 2009.67 915.16 2006.51 -0.5489E+01 0.8674E+01 -0.2636E+01 41 28.29 1995.39 936.76 1998.08 -0.5489E+01 0.7958E+01 -0.3732E+01 43 30.89 1981.11 956.67 1987.53 -0.5489E+01 0.7361E+01 -0.4310E+01 --------------------------------------------------------------------------------------------------




A.5 – 216


: :



4.7244"

------------------------------


End-plate extended on both tension & compression sides


1) 2)


Remark

Italy


R.Zandonini & P.Zanon (1987) EPB 1-2


Tested by Test Id.

V -109

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

9

27

36

cc

pc

li

pt

ct

54

63

72


45

Material : : :

gc


18

beam

gt

81

lp

90

nc

ni

nt

A.5 – 217


A3 = P3 =

2.040000 5

K = Q1 =

0.001633 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4228E+04 0.3421E+03 0.1037E+04 3 0.06 169.98 20.63 163.48 0.1762E+04 0.3420E+03 0.9853E+03 5 0.24 339.96 82.23 323.68 0.7843E+03 0.3402E+03 0.7989E+03 7 0.50 509.94 169.94 503.75 0.5710E+03 0.3334E+03 0.5962E+03 9 0.84 669.29 281.59 675.26 0.3864E+03 0.3144E+03 0.4158E+03 11 1.26 818.03 405.36 818.73 0.2957E+03 0.2761E+03 0.2838E+03 13 2.02 966.76 583.90 984.53 0.1841E+03 0.1967E+03 0.1723E+03 15 2.83 1115.49 717.07 1103.08 0.1841E+03 0.1381E+03 0.1278E+03 17 4.44 1264.22 888.21 1275.35 0.6136E+02 0.8255E+02 0.6842E+02 19 8.08 1418.90 1101.16 1424.85 0.2595E+02 0.4322E+02 0.2208E+02 21 11.31 1487.32 1218.42 1480.97 0.1884E+02 0.3081E+02 0.1600E+02 23 16.16 1561.69 1343.51 1566.91 0.1994E+02 0.2189E+02 0.1882E+02 25 19.39 1636.05 1408.38 1625.59 0.1871E+02 0.1848E+02 0.1700E+02 27 24.24 1695.55 1489.13 1694.74 0.9594E+01 0.1508E+02 0.1134E+02 29 28.28 1725.29 1545.94 1731.40 0.5521E+01 0.1314E+02 0.6996E+01 31 32.32 1740.16 1595.93 1753.04 0.4470E+01 0.1167E+02 0.3935E+01 33 37.71 1769.91 1654.64 1767.18 0.5522E+01 0.1020E+02 0.1587E+01 35 43.09 1784.78 1706.44 1772.33 0.1366E-13 0.9082E+01 0.4709E+00 37 48.48 1784.78 1752.91 1773.35 -0.1840E+01 0.8205E+01 -0.2554E-01 39 53.87 1764.95 1795.14 1772.56 -0.3681E+01 0.7496E+01 -0.2377E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.47635833E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.19627880E+04 -0.92608889E+04 0.22682472E+05 -0.14286554E+05 -0.12503519E+05 Rj0 = 0.0000 0.0010 4.4400 RKj = 0.10192511E+06 -0.10190452E+06 -0.20980010E+02



A.5 – 218


: :



4.7244"

------------------------------




1) 2)


Remark

Italy




Tested by Test Id.

V -110

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

4

12

16

cc

pc

li

pt

ct

24

28

32


20

Material : : :

gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 219


A3 = P3 =

2.040000 5

K = Q1 =

0.001464 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6533E+03 0.3816E+03 0.4366E+04 3 0.15 169.98 55.44 195.51 0.5004E+04 0.3809E+03 0.2438E+04 5 0.19 339.96 72.69 299.33 0.2889E+04 0.3803E+03 0.2151E+04 7 0.28 509.94 106.85 469.72 0.1703E+04 0.3787E+03 0.1656E+04 9 0.50 669.29 190.92 732.62 0.4772E+03 0.3718E+03 0.7611E+03 11 0.75 818.03 280.21 839.13 0.6503E+03 0.3581E+03 0.1615E+03 13 1.04 966.76 381.15 951.77 0.4568E+03 0.3327E+03 0.5702E+03 15 1.42 1115.49 500.43 1111.55 0.3764E+03 0.2886E+03 0.2994E+03 17 2.42 1264.22 732.17 1282.87 0.9204E+02 0.1825E+03 0.1058E+03 19 4.04 1412.95 951.84 1415.09 0.9204E+02 0.1026E+03 0.6738E+02 21 5.66 1512.11 1088.22 1506.13 0.3068E+02 0.7042E+02 0.4606E+02 23 7.27 1561.69 1187.31 1568.12 0.3068E+02 0.5380E+02 0.3214E+02 25 8.89 1611.26 1265.52 1614.11 0.3068E+02 0.4373E+02 0.2574E+02 27 10.77 1660.84 1340.25 1659.71 0.2301E+02 0.3607E+02 0.2316E+02 29 12.93 1710.42 1411.23 1708.54 0.2220E+02 0.3019E+02 0.2233E+02 31 14.87 1752.06 1465.93 1751.51 0.2147E+02 0.2642E+02 0.2201E+02 33 16.81 1793.71 1514.26 1793.94 0.2147E+02 0.2354E+02 0.2176E+02 35 18.75 1808.58 1557.62 1809.51 -0.6136E+01 0.2127E+02 -0.6382E+01 37 20.68 1796.68 1597.03 1796.99 -0.6136E+01 0.1943E+02 -0.6524E+01 39 22.62 1784.78 1633.19 1784.24 -0.6136E+01 0.1791E+02 -0.6618E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.22105833E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.13994857E+04 0.40835793E+04 -0.12968799E+05 0.19675116E+05 -0.14254777E+05 Rj0 = 0.0000 0.0010 0.8800 17.8000 RKj = -0.23731739E+06 0.23651831E+06 0.82027693E+03 -0.27948323E+02



A.5 – 220


: :



4.7244"

------------------------------




1) 2)


Remark

Italy




Tested by Test Id.

V -111

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

3

9

12

cc

pc

li

pt

ct

18

21

24


15

Material : : :

gc


6

beam

gt

27

lp

30

nc

ni

nt

A.5 – 221


A3 = P3 =

2.040000 5

K = Q1 =

0.001298 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3880E+04 0.4304E+03 0.4866E+04 3 0.05 178.48 21.09 197.23 0.8248E+04 0.4303E+03 0.4109E+04 5 0.09 356.96 38.73 354.20 0.2709E+04 0.4301E+03 0.3560E+04 7 0.15 535.44 64.79 548.35 0.3268E+04 0.4295E+03 0.2870E+04 9 0.22 713.91 94.06 721.88 0.2174E+04 0.4285E+03 0.2242E+04 11 0.30 892.39 130.53 885.83 0.1847E+04 0.4266E+03 0.1636E+04 13 0.40 1041.12 171.68 1018.32 0.1249E+04 0.4236E+03 0.1136E+04 15 0.58 1159.86 248.40 1167.52 0.4171E+03 0.4151E+03 0.5648E+03 17 0.97 1280.59 403.04 1287.85 0.2605E+03 0.3831E+03 0.1721E+03 19 1.94 1437.74 714.44 1426.22 0.1229E+03 0.2570E+03 0.1422E+03 21 2.83 1524.50 902.26 1534.42 0.9204E+02 0.1738E+03 0.9760E+02 23 3.64 1598.87 1023.69 1600.32 0.9203E+02 0.1305E+03 0.7036E+02 25 4.65 1673.23 1138.08 1667.39 0.6136E+02 0.9879E+02 0.6520E+02 27 5.86 1747.60 1243.08 1745.33 0.6136E+02 0.7645E+02 0.6179E+02 29 7.11 1808.58 1329.22 1814.90 0.3681E+02 0.6214E+02 0.4806E+02 31 8.40 1856.18 1402.75 1865.92 0.3681E+02 0.5223E+02 0.3116E+02 33 9.70 1903.77 1465.48 1897.19 0.2415E+02 0.4518E+02 0.1806E+02 35 10.91 1918.64 1517.09 1913.96 0.1227E+02 0.4018E+02 0.1027E+02 37 12.12 1933.52 1563.31 1923.42 0.9014E+00 0.3625E+02 0.5778E+01 39 13.20 1923.60 1600.77 1928.34 -0.9208E+01 0.3338E+02 0.3570E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12021667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = 0.10877717E+02 0.15772581E+05 -0.74966989E+05 0.16354001E+06 -0.16662334E+06 Rj0 = 0.0000 0.0010 RKj = -0.22203113E+05 0.22204129E+05



A.5 – 222


: :



4.7244"

------------------------------




1) 2)


Remark

Italy




Tested by Test Id.

V -112

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

3

9

12

cc

pc

li

pt

ct

18

21

24


15

Material : : :

gc


6

beam

gt

27

lp

30

nc

ni

nt

A.5 – 223


A3 = P3 =

2.040000 5

K = Q1 =

0.001202 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.18412500E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.49978100E+04 -0.20854607E+05 0.69186809E+05 -0.11739429E+06 0.93852283E+05 Rj0 = 0.0000 0.0010 0.1200 RKj = -0.18284392E+06 0.18015901E+06 0.26954054E+04



A.5 – 224


: :


Remark

1) 2)

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 66.37 0.04 3 136.05 0.09 4 199.10 0.14 5 268.78 0.29 6 338.47 0.42 7 398.20 0.54 8 466.22 0.70 9 532.59 0.86 10 598.95 1.04 11 666.98 1.25 12 728.37 1.44 13 794.73 1.67 14 871.05 2.02 15 939.08 2.39 16 1010.42 2.93 17 1071.81 3.43 18 1136.52 4.56 19 1159.75 5.66 20 1182.97 6.76 ------------------------------



Major parameters

1.25"

Brazil

pc =

1.4965"


L.F.L.Ribeiro & R.M.Goncalves (1996) CT1A-1

Column : CVS350x105 Beam : VS250x37 Plate thickness :

Tested by Test Id.

V -113

0 0.0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0.9

2.7

3.6

4.5

5.4

6.3

cc

pc

pic

pi pi

pit

pt

ct

7.2



1.8

beam

gt

8.1

li

9.0

nc

ni

nt

A.5 – 225


A3 = P3 =

2.040000 5

K = Q1 =

0.004091 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.66333333E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = 0.33229944E+03 0.14225995E+04 -0.15512702E+05 0.47356483E+05 -0.60907710E+05



A.5 – 226


: :


Remark

1) 2)

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 68.58 0.03 3 142.30 0.11 4 207.45 0.18 5 277.74 0.29 6 346.32 0.39 7 409.75 0.49 8 476.62 0.61 9 545.20 0.74 10 617.20 0.86 11 687.50 1.03 12 756.07 1.20 13 836.65 1.46 14 894.95 1.68 15 961.81 1.97 16 996.96 2.37 17 1032.10 2.76 18 1066.39 3.10 19 1100.68 3.45 ------------------------------



Major parameters

1.00"

Brazil

pc =

1.4965"




Tested by Test Id.

V -114

0 0.0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0.6

1.8

2.4

3.0

3.6

4.2

cc

pc

pic

pi pi

pit

pt

ct

4.8



1.2

beam

gt

5.4

li

6.0

nc

ni

nt

A.5 – 227


A3 = P3 =

2.040000 5

K = Q1 =

0.004677 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 228


: :


Remark

1) 2)




Major parameters

1.00"

Brazil

pc =

1.4965"




Tested by Test Id.

V -115

0 0.0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0.9

2.7

3.6

4.5

5.4

6.3

cc

pc

pic

pi pi

pit

pt

ct

7.2



1.8

beam

gt

8.1

li

9.0

nc

ni

nt

A.5 – 229


A3 = P3 =

2.040000 5

K = Q1 =

0.004677 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 230


: :


Remark

1) 2)




Major parameters

0.875"

Brazil

pc =

1.4965"




Tested by Test Id.

V -116

0 0.0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0.8

2.4

3.2

4.0

4.8

5.6

cc

pc

pic

pi pi

pit

pt

ct

6.4



1.6

beam

gt

7.2

li

8.0

nc

ni

nt

A.5 – 231


A3 = P3 =

2.040000 5

K = Q1 =

0.005067 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.55250000E-01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 0 AI = -0.66026774E+02 0.50804474E+04 -0.34404372E+05 0.90383888E+05 -0.10432098E+06



A.5 – 232


: :


Remark

1) 2)




Major parameters

0.875"

Brazil

pc =

1.4965"




Tested by Test Id.

V -117

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 233


A3 = P3 =

2.040000 5

K = Q1 =

0.005067 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 234


: :


Remark

1) 2)




Major parameters

0.75"

Brazil

pc =

1.7461"




Tested by Test Id.

V -118

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 235


A3 = P3 =

2.040000 5

K = Q1 =

0.005559 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 236


: :


Remark

1) 2)

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 199.10 0.03 3 298.65 0.08 4 404.83 0.15 5 502.72 0.24 6 600.61 0.36 7 696.84 0.55 8 796.39 0.84 9 894.28 1.19 10 997.15 1.66 11 1056.88 2.09 12 1143.15 2.97 13 1184.63 4.10 14 1221.13 5.18 15 1236.07 6.46 16 1239.38 8.04 ------------------------------



Major parameters

1.25"

Brazil

pc =

1.4965"


L.F.L.Ribeiro & R.M.Goncalves (1996) CT1B-1


Tested by Test Id.

V -119

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 237


A3 = P3 =

2.040000 5

K = Q1 =

0.004091 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6637E+04 0.1365E+03 0.5200E+04 2 0.03 199.10 4.10 136.60 0.4894E+04 0.1365E+03 0.3962E+04 3 0.08 298.65 10.92 296.01 0.1793E+04 0.1365E+03 0.2525E+04 4 0.15 404.83 20.48 428.31 0.1329E+04 0.1363E+03 0.1386E+04 5 0.24 502.72 32.74 519.51 0.9711E+03 0.1358E+03 0.7457E+03 6 0.36 600.61 48.96 590.42 0.6960E+03 0.1348E+03 0.5010E+03 7 0.55 696.84 74.35 679.82 0.4419E+03 0.1323E+03 0.4573E+03 8 0.84 796.39 111.84 802.25 0.3145E+03 0.1256E+03 0.3707E+03 9 1.19 894.28 153.77 906.48 0.2537E+03 0.1132E+03 0.2329E+03 10 1.66 997.15 202.30 992.17 0.1771E+03 0.9292E+02 0.1487E+03 11 2.09 1056.88 238.50 1049.65 0.1255E+03 0.7597E+02 0.1211E+03 12 2.97 1143.15 293.84 1143.34 0.7119E+02 0.5219E+02 0.7841E+02 13 4.10 1184.63 342.69 1198.11 0.3522E+02 0.3611E+02 0.2579E+02 14 5.18 1221.13 376.88 1215.63 0.2367E+02 0.2774E+02 0.1064E+02 15 6.46 1236.07 408.27 1227.71 0.7385E+01 0.2182E+02 0.9397E+01 16 8.04 1239.38 438.92 1243.80 0.2100E+01 0.1734E+02 0.1088E+02 --------------------------------------------------------------------------------------------------




A.5 – 238


: :


Remark

1) 2)

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 104.58 0.03 3 212.59 0.11 4 310.32 0.20 5 416.61 0.33 6 517.77 0.49 7 618.92 0.69 8 721.79 0.90 9 893.23 1.31 10 1032.10 1.67 11 1131.54 1.92 12 1268.70 2.33 13 1376.71 2.73 14 1448.71 3.14 15 1549.87 3.67 16 1623.59 4.10 17 1697.31 4.76 18 1724.74 5.42 19 1783.03 6.04 20 1803.61 6.56 21 1819.04 7.01 ------------------------------



Major parameters

1.00"

Brazil

pc =

1.7461"




Tested by Test Id.

V -120

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

1

3

4

5

6

7

8

cc

pc

pic

pi pi

pit

pt

ct



2

beam

gt

9

li

10

nc

ni

nt

A.5 – 239


A3 = P3 =

2.040000 5

K = Q1 =

0.004677 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 240


: :


Remark

1) 2)




Major parameters

1.00"

Brazil

pc =

1.7461"




Tested by Test Id.

V -121

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 241


A3 = P3 =

2.040000 5

K = Q1 =

0.004677 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 242


: :


Remark

1) 2)

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 146.98 0.18 3 275.58 0.42 4 410.87 0.70 5 541.15 1.01 6 671.42 1.34 7 800.03 1.73 8 942.00 2.25 9 1073.95 2.84 10 1202.55 3.68 11 1331.16 4.88 12 1416.34 6.08 13 1491.50 7.73 14 1536.59 9.27 15 1600.06 10.55 16 1628.46 12.08 ------------------------------



Major parameters

0.875"

Brazil

pc =

1.7461"




Tested by Test Id.

V -122

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 243


A3 = P3 =

2.040000 5

K = Q1 =

0.005067 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.8165E+03 0.1103E+03 0.8645E+03 2 0.18 146.98 19.83 138.37 0.6963E+03 0.1099E+03 0.6827E+03 3 0.42 275.58 46.05 281.69 0.5115E+03 0.1083E+03 0.5267E+03 4 0.70 410.87 75.89 414.61 0.4533E+03 0.1044E+03 0.4347E+03 5 1.01 541.15 107.19 541.35 0.4079E+03 0.9701E+02 0.3886E+03 6 1.34 671.42 137.50 664.40 0.3650E+03 0.8631E+02 0.3579E+03 7 1.73 800.03 168.50 796.69 0.3054E+03 0.7264E+02 0.3191E+03 8 2.25 942.00 202.08 946.84 0.2499E+03 0.5696E+02 0.2573E+03 9 2.84 1073.95 231.72 1077.99 0.1945E+03 0.4429E+02 0.1892E+03 10 3.68 1202.55 263.69 1205.83 0.1342E+03 0.3299E+02 0.1217E+03 11 4.88 1331.16 297.29 1322.20 0.8908E+02 0.2395E+02 0.8005E+02 12 6.08 1416.34 322.74 1408.01 0.6028E+02 0.1880E+02 0.6456E+02 13 7.73 1491.50 350.00 1500.44 0.3714E+02 0.1458E+02 0.4718E+02 14 9.27 1536.59 370.38 1560.20 0.4037E+02 0.1211E+02 0.3076E+02 15 10.55 1600.06 384.88 1592.17 0.3545E+02 0.1064E+02 0.1972E+02 16 12.08 1628.46 400.10 1614.89 0.1856E+02 0.9314E+01 0.1071E+02 --------------------------------------------------------------------------------------------------




A.5 – 244


: :


Remark

1) 2)

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------1 0.00 0.00 2 1.67 0.07 3 143.64 0.10 4 277.25 0.27 5 405.86 0.47 6 537.81 0.74 7 676.43 1.06 8 810.05 1.45 9 945.34 1.90 10 1070.60 2.41 11 1205.89 3.26 12 1329.49 4.66 13 1386.28 5.87 14 1458.09 7.91 15 1503.19 9.56 16 1534.92 11.64 17 1551.63 13.52 18 1563.32 15.58 19 1575.01 17.64 ------------------------------



Major parameters

0.875"

Brazil

pc =

1.7461"




Tested by Test Id.

V -123

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 245


A3 = P3 =

2.040000 5

K = Q1 =

0.005067 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 246


: :


Remark

1) 2)




Major parameters

0.75"

Brazil

pc =

1.7461"




Tested by Test Id.

V -124

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 247


A3 = P3 =

2.040000 5

K = Q1 =

0.005559 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 248


: :


Remark

1) 2)




Major parameters

1.5"

Brazil

pc =

2.0654"




Tested by Test Id.

V -125

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 249


A3 = P3 =

2.040000 5

K = Q1 =

0.001618 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 250


: :


Remark

1) 2)




Major parameters

1.25"

Brazil

pc =

2.0654"




Tested by Test Id.

V -126

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 251


A3 = P3 =

2.040000 5

K = Q1 =

0.001805 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 252


: :


Remark

1) 2)




Major parameters

1.25"

Brazil

pc =

2.0654"




Tested by Test Id.

V -127

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 253


A3 = P3 =

2.040000 5

K = Q1 =

0.001805 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 254


: :


Remark

1) 2)




Major parameters

1.00"

Brazil

pc =

2.0654"




Tested by Test Id.

V -128

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 255


A3 = P3 =

2.040000 5

K = Q1 =

0.002064 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.14516667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.57748394E+03 0.49251119E+04 0.29221423E+04 -0.44462986E+05 0.65714142E+05 Rj0 = 3.1000 RKj = 0.55079880E+02



A.5 – 256


: :


1) 2)

pc =

2.3150"

------------------------------




Remark


Major parameters

1.00"

Brazil

Fasteners: A325- -1"D 1 1/16" Oversize holes Material : A36 Fy = 36.24 ksi Fu = 57.99 ksi



Tested by Test Id.

V -129

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 257


A3 = P3 =

2.040000 5

K = Q1 =

0.002064 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 258


: :


1) 2)

pc =

2.3150"

------------------------------




Remark


Major parameters

0.875"

Brazil




Tested by Test Id.

V -130

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

pic

pi pi

pit

pt

ct

12

15

18

21

24



6

beam

gt

27

li

30

nc

ni

nt

A.5 – 259


A3 = P3 =

2.040000 5

K = Q1 =

0.002235 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 260


: :


1) 2)

pc =

2.0654"

------------------------------




Remark


Major parameters

1.5"

Brazil




Tested by Test Id.

V -131

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 261


A3 = P3 =

2.040000 5

K = Q1 =

0.001618 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 262


: :


Remark

1) 2)




Major parameters

1.25"

Brazil

pc =

2.0654"




Tested by Test Id.

V -132

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 263


A3 = P3 =

2.040000 5

K = Q1 =

0.001805 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 264


: :


1) 2)

pc =

2.0654"

------------------------------




Remark


Major parameters

1.25"

Brazil




Tested by Test Id.

V -133

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 265


A3 = P3 =

2.040000 5

K = Q1 =

0.001805 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 266


: :


Remark

1) 2)




Major parameters

1.00"

Brazil

pc =

2.0654"




Tested by Test Id.

V -134

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

pic

pi pi

pit

pt

ct

8

10

12

14

16



4

beam

gt

18

li

20

nc

ni

nt

A.5 – 267


A3 = P3 =

2.040000 5

K = Q1 =

0.002064 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 268


: :


1) 2)

pc =

2.3150"

------------------------------




Remark


Major parameters

1.00"

Brazil




Tested by Test Id.

V -135

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 269


A3 = P3 =

2.040000 5

K = Q1 =

0.002064 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 270


: :


1) 2)

pc =

2.3150"

------------------------------




Remark


Major parameters

0.875"

Brazil




Tested by Test Id.

V -136

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 271


A3 = P3 =

2.040000 5

K = Q1 =

0.002235 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.21741667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = -0.80018863E+03 0.75759677E+02 0.39119664E+05 -0.11812755E+06 0.11389702E+06 Rj0 = 8.2800 RKj = 0.40489105E+02



A.5 – 272


: :


1.8602"

------------------------------


End-plate: 640x200x20 mm Failure mode: End-plate fracture


1) 2)


Remark

U.K. Fasteners: G8.8- -M24 33/32" Oversize holes Material : S275 Fy = 43.66 ksi Fu = 70.49 ksi

Major parameters

B.Bose et al. (1996) 7

Column : 254x254 UC 89 Beam : 457x191 UB 74 Plate thickness : 20 mm

Tested by Test Id.

V -137

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

li

pt

ct

20

25

30

35

40

Material : S275 Fy = 43.66 ksi : Experimental : Polynominal : M. Exponential

gc


10

beam

gt

45

lp

50

nc

ni

nt

A.5 – 273


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 274


: :


= 13.2677" = 0.0000" = 3.5433" = 2 X 1 2

3.9370" 9.7244"

nc = 2 X

pc = pic=

------------------------------


End-plate: 640x200x15 mm Failure mode: Column web buckling


1) 2)


Remark


Major parameters

B.Bose et al. (1996) 11


Tested by Test Id.

V -138

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

li

pt

ct

16

20

24

28

32


gc


8

beam

gt

36

lp

40

nc

ni

nt

A.5 – 275


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7008E+03 0.6158E+03 0.1097E+04 3 0.50 350.42 309.24 316.82 0.5850E+03 0.6238E+03 0.4241E+03 5 1.25 650.78 791.30 683.78 0.4946E+03 0.6693E+03 0.5970E+03 7 1.61 939.65 1038.33 912.35 0.1581E+04 0.7096E+03 0.6625E+03 9 2.02 1211.78 1342.92 1186.63 0.3448E+03 0.7765E+03 0.6633E+03 11 2.53 1468.85 1768.03 1507.70 0.7334E+03 0.8978E+03 0.5851E+03 13 3.14 1819.78 2366.21 1822.36 0.5218E+03 0.1049E+04 0.4432E+03 15 4.00 2048.09 3206.94 2049.12 0.9819E+02 0.8078E+03 0.1279E+03 17 6.00 2188.49 4192.78 2206.76 0.7048E+02 0.3111E+03 0.7934E+02 19 8.00 2326.80 4674.50 2324.33 0.5424E+02 0.1909E+03 0.5010E+02 21 10.00 2424.75 4999.57 2422.15 0.4175E+02 0.1401E+03 0.4753E+02 23 12.00 2464.29 5249.15 2458.91 0.8598E+01 0.1119E+03 0.1474E+02 25 14.00 2477.48 5453.62 2480.52 0.5937E+01 0.9379E+02 0.7121E+01 27 16.00 2485.90 5627.87 2489.20 0.2606E+01 0.8115E+02 0.2095E+01 29 18.00 2489.73 5780.38 2490.86 0.1460E+01 0.7179E+02 -0.2033E-01 31 20.00 2491.15 5916.43 2490.39 0.2359E+00 0.6454E+02 -0.2309E+00 33 22.00 2491.61 6039.52 2490.52 0.4270E+00 0.5876E+02 0.4427E+00 35 24.00 2492.93 6152.16 2492.31 0.1328E+01 0.5402E+02 0.1351E+01 37 26.00 2495.58 6256.14 2495.87 0.8706E+00 0.5007E+02 0.2182E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.27916667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.46357451E+04 -0.44798500E+05 0.14376184E+06 -0.22131829E+06 0.17262680E+06 Rj0 = 3.4500 5.0000 10.0000 RKj = -0.12710724E+03 0.15737161E+03 -0.26136579E+02



A.5 – 276


: :


= 13.2677" = 0.0000" = 3.5433" = 2 X 1 2

3.9370" 9.7244"

nc = 2 X

pc = pic=

------------------------------


End-plate: 640x200x15 mm Failure mode: Column web buckling and end-plate fracture


1) 2)


Remark


Major parameters

B.Bose et al. (1996) 12


Tested by Test Id.

V -139

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

10

30

40

50

60

70

cc

pc

li

pt

ct

80


gc


20

beam

gt

90

lp

100

nc

ni

nt

A.5 – 277


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 278


: :


= 24.9606" = 0.0000" = 3.5433" = 2 X 1 nc = 2 X

2

pc = 3.9370" pic= 21.4173"

------------------------------




1) 2)


Remark


Major parameters

B.Bose et al. (1996) 13


Tested by Test Id.

V -140

0

750

1500

2250

3000

3750

4500

5250

6000

6750

7500

tp

column

Moment ( kip-inch )


0

3

9

cc

pc

li

pt

ct

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.5 – 279


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 280


: :


= 13.2677" = 0.0000" = 3.5433" = 2 X 1 2

3.9370" 9.7244"

nc = 2 X

pc = pic=

------------------------------


End-plate: 640x200x15 mm Failure mode: Bolt fracture


1) 2)


Remark


Major parameters

B.Bose et al. (1996) 14


Tested by Test Id.

V -141

0

450

900

1350

1800

2250

2700

3150

3600

4050

4500

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 281


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3472E+03 0.6158E+03 -0.9997E+02 3 0.99 365.30 620.15 386.46 0.4758E+03 0.6483E+03 0.6174E+03 5 1.99 947.24 1319.67 983.31 0.6459E+03 0.7708E+03 0.5330E+03 7 2.48 1281.24 1723.48 1223.61 0.5952E+03 0.8841E+03 0.4481E+03 9 3.97 1692.72 3181.62 1734.82 0.2399E+03 0.8228E+03 0.2603E+03 11 5.96 2155.74 4180.25 2139.80 0.1738E+03 0.3152E+03 0.1650E+03 13 7.95 2416.89 4664.92 2426.54 0.1193E+03 0.1927E+03 0.1266E+03 15 9.93 2647.23 4989.72 2649.68 0.1083E+03 0.1414E+03 0.9986E+02 17 11.92 2829.36 5240.17 2827.05 0.8007E+02 0.1128E+03 0.7951E+02 19 13.90 2978.07 5444.20 2969.67 0.6498E+02 0.9454E+02 0.6547E+02 21 15.89 3089.56 5618.91 3089.85 0.5362E+02 0.8175E+02 0.5589E+02 23 17.88 3196.93 5771.74 3193.78 0.4903E+02 0.7228E+02 0.4883E+02 25 19.86 3279.62 5907.36 3284.47 0.3723E+02 0.6500E+02 0.4288E+02 27 21.85 3360.22 6030.68 3364.17 0.4695E+02 0.5915E+02 0.3726E+02 29 23.84 3437.45 6143.49 3432.88 0.2785E+02 0.5437E+02 0.3183E+02 31 25.82 3482.16 6247.10 3490.76 0.2104E+02 0.5040E+02 0.2669E+02 33 27.81 3527.57 6343.93 3539.04 0.2380E+02 0.4701E+02 0.2191E+02 35 29.79 3576.60 6434.08 3578.15 0.2575E+02 0.4411E+02 0.1768E+02 37 31.78 3621.28 6520.53 3609.58 0.1712E+02 0.4154E+02 0.1402E+02 39 33.77 3651.58 6600.29 3634.32 0.9700E+01 0.3933E+02 0.1094E+02 41 35.75 3657.10 6675.65 3653.42 0.5091E+00 0.3737E+02 0.8442E+01 43 37.74 3657.52 6749.10 3668.14 0.5300E+00 0.3559E+02 0.6429E+01 --------------------------------------------------------------------------------------------------




A.5 – 282


: :


1) 2)

li pi gc ni

= 24.9606" = 0.0000" = 3.5433" = 2 X 1 nc = 2 X

2

pc = 3.9370" pic= 21.4173"


End-plate: 930x250x15 mm Failure mode: Bolt fracture, thread stripping and end-plate fracture


Remark


Major parameters

B.Bose et al. (1996) 15


Tested by Test Id.

V -142

0

750

1500

2250

3000

3750

4500

5250

6000

6750

7500

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

li

pt

ct

8

10

12

14

16


gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 283


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 284


: :


3.9370"

------------------------------


End-plate: 640x200x15 mm Failure mode: Bolt fracture and End-plate fracture


1) 2)


Remark


Major parameters

B.Bose et al. (1996) 16


Tested by Test Id.

V -143

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

6

18

cc

pc

li

pt

ct

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.5 – 285


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 286


: :


= 13.2677" = 0.0000" = 3.5433" = 2 X 1 2

3.9370" 9.7244"

nc = 2 X

pc = pic=

------------------------------


End-plate: 640x200x15 mm Failure mode: Thread stripping


1) 2)


Remark


Major parameters

B.Bose et al. (1996) 17


Tested by Test Id.

V -144

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

2

6

cc

pc

li

pt

ct

8

10

12

14

16


gc


4

beam

gt

18

lp

20

nc

ni

nt

A.5 – 287


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 288


: :


1) 2)

li pi gc ni

= 21.9646" = 14.8780" = 3.5433" = 2 X 2




Remark

U.K.

2

3.9370" 3.5433"

nc = 2 X

pc = pic=

Fasteners: G8.8- -M24 33/32" Oversize holes Material : S275 Fy = 43.51 ksi Fu = 67.30 ksi

Major parameters

B.Bose et al. (1996) 18


Tested by Test Id.

V -145

0 0.0

600

1200

1800

2400

3000

3600

4200

4800

5400

6000

tp

column

Moment ( kip-inch )


0.9

2.7

3.6

4.5

5.4

6.3

cc

pc

li

pt

ct

7.2


gc


1.8

beam

gt

8.1

lp

9.0

nc

ni

nt

A.5 – 289


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 290


: :



1.5472"

------------------------------


End-plate: 400x150x10 mm Failure mode: Weld failure of assembly beam-end plate


1) 2)


Remark

Portugal


Ana M. Girao Coelho et al. (2004) FS1a

Column : HE340M Beam : IPE300 Plate thickness : 10 mm

Tested by Test Id.

V -146

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

10

30

40

50

60

70

cc

pc

pic

pi pi

pit

pt

ct

80



20

beam

gt

90

li

100

nc

ni

nt

A.5 – 291


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.5591E+03 0.9609E+02 0.4481E+03 3 0.22 122.99 21.15 90.72 0.4894E+03 0.9633E+02 0.3788E+03 5 1.00 312.05 97.78 316.12 0.2093E+03 0.1013E+03 0.2174E+03 7 1.97 476.53 203.51 474.71 0.1463E+03 0.1197E+03 0.1226E+03 9 3.95 648.61 493.85 640.37 0.7062E+02 0.1299E+03 0.5967E+02 11 7.89 801.83 726.02 802.66 0.2487E+02 0.3042E+02 0.2820E+02 13 11.84 878.52 816.28 884.76 0.1798E+02 0.1773E+02 0.1559E+02 15 15.78 942.03 875.33 939.19 0.1480E+02 0.1285E+02 0.1309E+02 17 19.73 997.84 920.41 991.86 0.1345E+02 0.1021E+02 0.1364E+02 19 23.68 1048.84 957.22 1045.75 0.1223E+02 0.8539E+01 0.1340E+02 21 27.62 1092.55 988.46 1095.77 0.1027E+02 0.7382E+01 0.1180E+02 23 31.57 1130.90 1015.85 1137.87 0.8873E+01 0.6526E+01 0.9452E+01 25 35.51 1161.29 1040.21 1170.31 0.7474E+01 0.5867E+01 0.7048E+01 27 39.46 1194.44 1062.30 1193.90 0.7452E+01 0.5340E+01 0.4972E+01 29 43.41 1218.30 1082.72 1210.21 0.3707E+01 0.4905E+01 0.3363E+01 31 47.35 1221.24 1101.30 1221.04 0.1207E+01 0.4547E+01 0.2205E+01 33 51.30 1231.18 1118.63 1228.07 0.1600E+01 0.4243E+01 0.1408E+01 35 55.24 1233.20 1134.81 1232.51 0.6929E+00 0.3981E+01 0.8815E+00 37 59.19 1248.57 1150.07 1235.27 0.6586E+01 0.3753E+01 0.5422E+00 39 63.14 1255.73 1164.45 1236.96 -0.2222E+02 0.3553E+01 0.3291E+00 41 65.11 1191.15 1171.40 1237.53 -0.3262E+02 0.3461E+01 0.2554E+00 --------------------------------------------------------------------------------------------------




A.5 – 292


: :



1.5472"

------------------------------


End-plate: 400x150x10 mm Failure mode: Weld failure of the assembly beam-end plate


1) 2)


Remark

Portugal


Ana M. Girao Coelho et al. (2004) FS1b


Tested by Test Id.

V -147

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

13

39

52

65

78

91

cc

pc

pic

pi pi

pit

pt

ct

li

nc

ni

nt

104 117 130



26

beam

gt

A.5 – 293


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1750E+03 0.9609E+02 0.1664E+03 2 0.50 87.50 48.25 86.07 0.1750E+03 0.9733E+02 0.1753E+03 3 1.00 175.01 97.78 173.37 0.1670E+03 0.1013E+03 0.1723E+03 4 1.48 251.44 147.90 254.01 0.1576E+03 0.1082E+03 0.1629E+03 5 1.97 327.87 203.51 330.67 0.1507E+03 0.1197E+03 0.1497E+03 6 2.48 401.88 268.90 403.12 0.1451E+03 0.1379E+03 0.1343E+03 7 2.99 475.88 344.91 467.68 0.1270E+03 0.1596E+03 0.1189E+03 8 3.94 564.42 492.53 567.71 0.8647E+02 0.1307E+03 0.9240E+02 9 4.98 646.68 594.11 651.05 0.7468E+02 0.7251E+02 0.6891E+02 10 5.90 711.79 649.27 706.85 0.6043E+02 0.5017E+02 0.5312E+02 11 7.87 787.21 725.41 788.08 0.3189E+02 0.3054E+02 0.3174E+02 12 9.84 837.42 776.55 838.89 0.2346E+02 0.2232E+02 0.2108E+02 13 13.78 913.81 847.69 911.40 0.1721E+02 0.1489E+02 0.1782E+02 14 17.71 972.91 898.79 974.03 0.1409E+02 0.1138E+02 0.1438E+02 15 21.65 1024.68 939.17 1026.10 0.1255E+02 0.9311E+01 0.1218E+02 16 25.59 1071.80 972.95 1070.87 0.1098E+02 0.7930E+01 0.1064E+02 17 29.52 1111.13 1002.06 1110.45 0.9504E+01 0.6940E+01 0.9559E+01 18 33.46 1146.58 1027.86 1146.46 0.8754E+01 0.6190E+01 0.8753E+01 19 37.40 1180.12 1051.04 1179.63 0.8061E+01 0.5601E+01 0.8108E+01 20 41.33 1210.03 1072.09 1210.39 0.7305E+01 0.5126E+01 0.7560E+01 21 45.27 1237.60 1091.48 1239.22 0.7184E+01 0.4732E+01 0.7084E+01 22 49.21 1266.64 1109.46 1266.30 0.6943E+01 0.4401E+01 0.6673E+01 23 53.14 1292.25 1126.18 1291.82 0.6184E+01 0.4118E+01 0.6327E+01 24 57.08 1315.30 1141.91 1316.17 0.6056E+01 0.3873E+01 0.6042E+01 25 61.02 1339.97 1156.74 1339.51 0.6093E+01 0.3659E+01 0.5813E+01 26 64.95 1363.25 1170.74 1361.99 0.5625E+01 0.3470E+01 0.5634E+01 27 68.89 1384.24 1184.08 1383.90 0.5237E+01 0.3301E+01 0.5497E+01 28 72.83 1404.52 1196.78 1405.35 0.5152E+01 0.3150E+01 0.5393E+01 29 77.05 1426.28 1209.76 1426.42 -0.1083E+02 0.3005E+01 -0.2467E+02 30 80.70 1336.28 1220.73 1336.28 -0.2466E+02 0.2888E+01 -0.2472E+02 --------------------------------------------------------------------------------------------------




A.5 – 294


: :



1.5472"

------------------------------


End-plate: 400x150x15 mm Failure mode: Nut stripping of bolt #4 and weld failure


1) 2)


Remark

Portugal




Tested by Test Id.

V -148

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 295


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2213E+03 0.1113E+03 0.1840E+03 2 0.50 110.64 55.88 108.73 0.2352E+03 0.1127E+03 0.2393E+03 3 1.00 235.24 113.24 231.12 0.2311E+03 0.1173E+03 0.2449E+03 4 1.50 341.76 173.80 350.16 0.2159E+03 0.1257E+03 0.2291E+03 5 2.01 453.35 241.26 461.17 0.2242E+03 0.1400E+03 0.2057E+03 6 2.51 568.09 316.23 558.15 0.1941E+03 0.1612E+03 0.1824E+03 7 3.01 647.47 403.16 644.04 0.1550E+03 0.1856E+03 0.1616E+03 8 4.01 794.99 580.89 788.46 0.1271E+03 0.1451E+03 0.1293E+03 9 5.01 901.76 690.54 905.97 0.1002E+03 0.8280E+02 0.1071E+03 10 6.02 996.32 758.78 1005.54 0.9088E+02 0.5585E+02 0.9084E+02 11 7.02 1084.47 807.40 1089.80 0.8379E+02 0.4236E+02 0.7810E+02 12 8.02 1163.90 845.39 1162.38 0.7105E+02 0.3437E+02 0.6731E+02 13 9.02 1226.58 876.91 1224.87 0.6237E+02 0.2905E+02 0.5788E+02 14 10.03 1289.26 904.21 1279.04 0.5470E+02 0.2522E+02 0.4958E+02 15 12.03 1369.52 949.22 1364.39 0.3431E+02 0.2015E+02 0.3649E+02 16 14.04 1426.73 986.20 1427.96 0.2531E+02 0.1689E+02 0.2736E+02 17 16.04 1471.10 1017.58 1476.22 0.2072E+02 0.1463E+02 0.2132E+02 18 18.05 1509.78 1045.20 1514.74 0.1830E+02 0.1294E+02 0.1727E+02 19 20.05 1544.48 1069.71 1546.31 0.1502E+02 0.1163E+02 0.1445E+02 20 22.06 1569.98 1092.01 1573.09 0.1211E+02 0.1059E+02 0.1227E+02 21 24.07 1593.17 1112.41 1595.89 0.1077E+02 0.9735E+01 0.1047E+02 22 26.07 1613.18 1131.15 1615.21 0.9512E+01 0.9025E+01 0.8882E+01 23 28.08 1631.31 1148.66 1631.60 0.7879E+01 0.8419E+01 0.7455E+01 24 30.08 1644.80 1164.97 1645.22 0.7648E+01 0.7900E+01 0.6185E+01 25 32.09 1662.00 1180.38 1656.50 0.8982E+01 0.7446E+01 0.5061E+01 26 34.09 1680.80 1194.87 1665.62 0.6583E+01 0.7049E+01 0.4093E+01 27 36.10 1688.34 1208.68 1673.00 0.3758E+01 0.6695E+01 0.3267E+01 28 38.10 1695.87 1221.75 1678.83 0.3200E+01 0.6380E+01 0.2583E+01 29 40.11 1701.16 1234.28 1683.43 0.3700E+01 0.6095E+01 0.2020E+01 30 41.72 1708.50 1244.09 1686.38 -0.1698E+02 0.5884E+01 0.1648E+01 31 42.92 1668.85 1250.90 1688.21 -0.3304E+02 0.5742E+01 0.1411E+01 32 44.12 1629.20 1257.79 1689.78 -0.3304E+02 0.5603E+01 0.1205E+01 --------------------------------------------------------------------------------------------------




A.5 – 296


: :



1.5472"

------------------------------


End-plate: 400x150x15 mm Failure mode: Nut stripping of bolt #1 and #4


1) 2)


Remark

Portugal




Tested by Test Id.

V -149

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 297


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2226E+03 0.1113E+03 0.2363E+03 2 0.50 111.32 55.88 114.09 0.2226E+03 0.1127E+03 0.2213E+03 3 1.00 222.63 113.24 222.07 0.2138E+03 0.1173E+03 0.2110E+03 4 1.52 329.03 176.32 329.25 0.2046E+03 0.1262E+03 0.2012E+03 5 2.04 435.44 245.48 431.23 0.1874E+03 0.1410E+03 0.1909E+03 6 2.52 517.77 317.85 520.42 0.1734E+03 0.1617E+03 0.1806E+03 7 2.99 600.11 399.46 602.78 0.1711E+03 0.1848E+03 0.1698E+03 8 3.54 691.55 503.13 692.62 0.1678E+03 0.1828E+03 0.1568E+03 9 4.08 783.00 590.99 773.82 0.1516E+03 0.1390E+03 0.1440E+03 10 4.99 893.70 688.86 895.31 0.1160E+03 0.8359E+02 0.1233E+03 11 6.13 1017.98 764.82 1022.40 0.9970E+02 0.5395E+02 0.1003E+03 12 6.98 1096.82 805.62 1101.36 0.8639E+02 0.4279E+02 0.8585E+02 13 8.17 1189.02 850.53 1193.29 0.7295E+02 0.3343E+02 0.6933E+02 14 10.21 1322.02 908.93 1312.87 0.5407E+02 0.2462E+02 0.4945E+02 15 12.25 1409.63 953.61 1400.01 0.3564E+02 0.1972E+02 0.3692E+02 16 14.29 1467.43 990.38 1466.43 0.2574E+02 0.1657E+02 0.2873E+02 17 16.34 1514.87 1021.93 1519.07 0.2153E+02 0.1434E+02 0.2292E+02 18 18.38 1555.54 1049.43 1561.18 0.1771E+02 0.1270E+02 0.1854E+02 19 20.42 1587.13 1073.98 1595.28 0.1449E+02 0.1142E+02 0.1501E+02 20 22.46 1614.64 1096.21 1622.83 0.1255E+02 0.1041E+02 0.1209E+02 21 24.50 1638.31 1116.56 1644.94 0.1127E+02 0.9572E+01 0.9658E+01 22 26.54 1660.61 1135.36 1662.52 0.1068E+02 0.8875E+01 0.7639E+01 23 28.59 1682.00 1152.92 1676.41 0.8834E+01 0.8280E+01 0.5974E+01 24 30.63 1696.78 1169.28 1687.18 0.6903E+01 0.7770E+01 0.4633E+01 25 32.67 1710.16 1184.67 1695.50 0.5940E+01 0.7326E+01 0.3560E+01 26 34.71 1721.01 1199.21 1701.86 0.5205E+01 0.6935E+01 0.2713E+01 27 36.75 1731.40 1212.99 1706.69 0.4504E+01 0.6589E+01 0.2052E+01 28 38.80 1739.42 1226.18 1710.35 0.4226E+01 0.6278E+01 0.1539E+01 29 40.30 1746.11 1235.59 1712.43 -0.2235E+02 0.6067E+01 0.1243E+01 30 41.59 1687.55 1243.16 1713.89 -0.4539E+02 0.5904E+01 0.1031E+01 31 42.88 1628.99 1250.77 1715.10 -0.4539E+02 0.5745E+01 0.8536E+00 --------------------------------------------------------------------------------------------------




A.5 – 298


: :



1.5472"

------------------------------


End-plate: 400x150x20 mm Failure mode: Nut stripping of bolt #3 and #4 and some weld failure


1) 2)


Remark

Portugal




Tested by Test Id.

V -150

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 299


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2652E+03 0.1249E+03 0.2558E+03 3 1.00 257.01 127.06 256.23 0.2364E+03 0.1316E+03 0.2381E+03 5 2.00 473.68 269.16 473.42 0.1982E+03 0.1567E+03 0.2004E+03 7 3.00 659.11 450.31 663.38 0.1854E+03 0.2078E+03 0.1812E+03 9 4.00 841.20 650.23 836.35 0.1714E+03 0.1638E+03 0.1643E+03 11 6.00 1123.16 850.17 1122.18 0.1110E+03 0.6308E+02 0.1200E+03 13 8.00 1307.56 947.85 1318.50 0.7733E+02 0.3871E+02 0.7850E+02 15 10.00 1445.61 1013.77 1446.85 0.6418E+02 0.2841E+02 0.5246E+02 17 12.00 1551.24 1064.37 1536.87 0.3877E+02 0.2268E+02 0.3913E+02 19 14.00 1613.78 1105.83 1607.58 0.2919E+02 0.1902E+02 0.3222E+02 21 16.00 1666.89 1141.17 1667.19 0.2302E+02 0.1646E+02 0.2755E+02 23 18.00 1689.64 1172.09 1718.04 0.1504E+02 0.1456E+02 0.2333E+02 25 20.00 1752.96 1199.68 1760.53 0.3619E+02 0.1309E+02 0.1917E+02 27 21.64 1814.99 1220.43 1789.27 -0.4125E+04 0.1210E+02 0.1591E+02 29 22.00 1745.87 1224.78 1769.55 0.1442E+03 0.1191E+02 0.2548E+03 31 24.00 1785.71 1247.71 1772.11 0.1213E+02 0.1095E+02 -0.4389E+00 33 26.00 1777.47 1268.76 1768.17 -0.1762E+02 0.1015E+02 -0.3395E+01 35 28.00 1738.94 1288.34 1758.92 -0.2149E+02 0.9467E+01 -0.5761E+01 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.35833333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.53240204E+03 0.10285404E+05 -0.57414723E+05 0.13409549E+06 -0.14167113E+06 Rj0 = 21.6400 21.6700 22.0000 RKj = -0.34789284E+04 0.37184686E+04 -0.25169043E+03



A.5 – 300


: :



1.5472"

------------------------------


End-plate: 400x150x20 mm Failure mode: Nut stripping of bolt #3


1) 2)


Remark

Portugal




Tested by Test Id.

V -151

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 301


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2318E+03 0.1249E+03 0.2557E+03 3 0.98 235.29 124.44 228.53 0.2196E+03 0.1313E+03 0.2259E+03 5 1.96 454.79 262.92 448.58 0.2421E+03 0.1552E+03 0.2208E+03 7 2.93 645.51 435.87 653.82 0.1777E+03 0.2046E+03 0.2001E+03 9 3.91 838.93 635.00 835.90 0.1904E+03 0.1728E+03 0.1711E+03 11 5.87 1112.79 841.79 1117.32 0.1153E+03 0.6585E+02 0.1191E+03 13 7.83 1316.26 941.17 1315.38 0.8702E+02 0.3998E+02 0.8580E+02 15 9.78 1460.52 1007.43 1461.03 0.6540E+02 0.2924E+02 0.6498E+02 17 11.74 1574.20 1058.40 1573.05 0.4955E+02 0.2328E+02 0.5001E+02 19 13.69 1660.86 1099.86 1658.70 0.3888E+02 0.1950E+02 0.3825E+02 21 15.65 1727.97 1135.34 1723.95 0.2750E+02 0.1685E+02 0.2867E+02 23 17.61 1766.48 1166.35 1772.36 0.1853E+02 0.1489E+02 0.2104E+02 25 19.56 1801.26 1193.86 1807.39 0.1699E+02 0.1338E+02 0.1516E+02 27 21.52 1831.98 1218.86 1832.53 0.1187E+02 0.1217E+02 0.1072E+02 29 23.48 1850.07 1241.72 1850.19 0.9276E+01 0.1119E+02 0.7473E+01 31 25.43 1868.16 1262.71 1862.38 0.9239E+01 0.1037E+02 0.5159E+01 33 27.39 1883.92 1282.33 1870.79 0.5297E+01 0.9669E+01 0.3522E+01 35 29.35 1891.28 1300.68 1876.51 0.6796E+01 0.9068E+01 0.2386E+01 37 31.30 1864.43 1317.84 1880.36 -0.2704E+02 0.8548E+01 0.1610E+01 --------------------------------------------------------------------------------------------------




A.5 – 302


: :



1.5472"

------------------------------


End-plate: 400x150x10 mm Failure mode: Fracture of bolt #4 and some weld failure


1) 2)


Remark

Portugal




Tested by Test Id.

V -152

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

9

27

cc

pc

pic

pi pi

pit

pt

ct

36

45

54

63

72

Material : S690 Fy = 101.32ksi : Experimental : Polynominal : M. Exponential


18

beam

gt

81

li

90

nc

ni

nt

A.5 – 303


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2064E+03 0.9483E+02 0.2321E+03 2 1.01 208.51 97.49 201.69 0.1789E+03 0.1000E+03 0.1764E+03 3 2.01 360.23 205.52 365.74 0.1503E+03 0.1193E+03 0.1544E+03 4 3.02 510.52 344.85 514.77 0.1447E+03 0.1584E+03 0.1412E+03 5 4.03 652.60 497.46 651.22 0.1333E+03 0.1222E+03 0.1289E+03 6 5.04 779.89 590.51 774.77 0.1144E+03 0.6956E+02 0.1156E+03 7 6.04 882.85 647.50 883.57 0.9961E+02 0.4729E+02 0.1020E+03 8 7.05 980.04 689.06 979.65 0.8962E+02 0.3584E+02 0.8840E+02 9 9.06 1133.72 748.18 1132.61 0.6540E+02 0.2460E+02 0.6470E+02 10 11.08 1243.38 791.74 1244.22 0.4626E+02 0.1895E+02 0.4682E+02 11 13.09 1320.31 826.13 1325.20 0.3476E+02 0.1557E+02 0.3457E+02 12 15.11 1383.37 855.12 1386.23 0.2912E+02 0.1328E+02 0.2643E+02 13 17.12 1437.70 880.08 1433.64 0.2229E+02 0.1164E+02 0.2110E+02 14 19.14 1473.09 902.26 1472.36 0.1730E+02 0.1039E+02 0.1746E+02 15 21.15 1507.41 922.11 1504.72 0.1503E+02 0.9403E+01 0.1486E+02 16 23.16 1533.51 940.19 1532.49 0.1295E+02 0.8608E+01 0.1284E+02 17 25.18 1559.60 956.89 1556.69 0.1129E+02 0.7947E+01 0.1116E+02 18 27.19 1579.04 972.29 1577.64 0.8966E+01 0.7393E+01 0.9712E+01 19 29.21 1595.72 986.73 1595.93 0.7944E+01 0.6916E+01 0.8414E+01 20 31.22 1611.07 1000.21 1611.65 0.5881E+01 0.6506E+01 0.7254E+01 21 33.24 1619.39 1012.98 1625.23 0.4131E+01 0.6145E+01 0.6209E+01 22 35.25 1627.71 1025.00 1636.76 0.4535E+01 0.5828E+01 0.5283E+01 23 37.70 1640.00 1038.86 1648.47 0.3537E+00 0.5488E+01 0.4301E+01 24 39.28 1635.81 1047.53 1637.26 -0.3034E+01 0.5287E+01 -0.7366E+01 25 41.29 1628.74 1057.77 1621.82 -0.5563E+01 0.5063E+01 -0.7982E+01 26 43.31 1613.35 1067.78 1605.14 -0.7901E+01 0.4854E+01 -0.8513E+01 27 45.32 1596.90 1077.54 1587.57 -0.9280E+01 0.4662E+01 -0.8963E+01 28 47.34 1575.93 1086.59 1569.07 -0.1056E+02 0.4491E+01 -0.9344E+01 29 49.35 1554.35 1095.62 1549.96 -0.1242E+02 0.4329E+01 -0.9661E+01 30 51.37 1525.85 1104.06 1530.16 -0.1415E+02 0.4184E+01 -0.9927E+01 31 53.38 1497.35 1112.47 1509.98 -0.1418E+02 0.4046E+01 -0.1015E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.69733333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.49227858E+03 -0.41252348E+04 0.90436386E+04 -0.21140945E+04 -0.97447298E+04 Rj0 = 37.7000 RKj = -0.11115117E+02



A.5 – 304


: :



1.5472"

------------------------------


End-plate: 400x150x10 mm Failure mode: Fracture of bolt #3


1) 2)


Remark

Portugal




Tested by Test Id.

V -153

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

10

30

40

50

60

70

cc

pc

pic

pi pi

pit

pt

ct

80



20

beam

gt

90

li

100

nc

ni

nt

A.5 – 305


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1706E+03 0.9483E+02 0.1577E+03 3 1.99 344.53 203.15 344.52 0.1696E+03 0.1187E+03 0.1710E+03 5 3.99 655.12 492.43 653.08 0.1348E+03 0.1252E+03 0.1357E+03 7 5.98 885.57 644.63 887.44 0.1013E+03 0.4821E+02 0.1010E+03 9 7.97 1063.25 718.88 1060.42 0.7466E+02 0.2956E+02 0.7419E+02 11 9.97 1189.31 769.17 1188.04 0.5821E+02 0.2165E+02 0.5449E+02 13 13.95 1349.61 839.03 1351.39 0.2636E+02 0.1450E+02 0.3029E+02 15 17.94 1440.02 889.39 1445.35 0.2141E+02 0.1109E+02 0.1826E+02 17 21.92 1507.75 929.23 1505.39 0.1202E+02 0.9080E+01 0.1263E+02 19 25.91 1551.73 962.61 1549.84 0.1171E+02 0.7735E+01 0.9958E+01 21 29.90 1589.52 991.45 1586.36 0.7013E+01 0.6769E+01 0.8450E+01 23 33.88 1618.56 1016.88 1617.63 0.7342E+01 0.6040E+01 0.7288E+01 25 37.87 1641.75 1039.79 1644.51 0.4386E+01 0.5466E+01 0.6189E+01 27 41.86 1653.94 1060.64 1667.05 0.2684E+01 0.5002E+01 0.5118E+01 29 45.84 1656.36 1079.76 1659.71 -0.3040E+01 0.4619E+01 -0.8794E+01 31 49.83 1632.57 1097.53 1622.79 -0.8713E+01 0.4296E+01 -0.9688E+01 33 53.81 1592.41 1114.07 1582.68 -0.1109E+02 0.4021E+01 -0.1044E+02 35 57.80 1546.57 1129.62 1539.74 -0.1169E+02 0.3781E+01 -0.1106E+02 37 61.79 1490.26 1144.49 1494.59 -0.1891E+02 0.3569E+01 -0.1155E+02 --------------------------------------------------------------------------------------------------




A.5 – 306


: :


Major parameters

1) 2)


End-plate: 435x300x15 mm


Remark

Portugal

pc =

2.6476"

Fasteners: 12.9- -M24 33/32" Oversize holes Material : S690 Fy = 112.26 ksi Fu = 118.06 ksi

Ana M. Girao Coelho et al. (2007) EEP_15_2

Column : HE300M Beam : HE320A Plate thickness : 15 mm

Tested by Test Id.

V -154

0

400

800

1200

1600

2000

2400

2800

3200

3600

4000

tp

column

Moment ( kip-inch )


0

4

12

cc

pc

pic

pi pi

pit

pt

ct

16

20

24

28

32



8

beam

gt

36

li

40

nc

ni

nt

A.5 – 307


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2669E+03 0.1448E+03 0.3822E+03 2 0.97 258.93 142.72 268.95 0.2717E+03 0.1521E+03 0.2363E+03 3 1.94 527.10 301.12 514.71 0.2911E+03 0.1790E+03 0.2783E+03 4 2.91 823.75 500.17 806.62 0.2935E+03 0.2359E+03 0.3179E+03 5 3.89 1099.10 731.31 1121.99 0.2921E+03 0.2030E+03 0.3194E+03 6 4.86 1393.04 881.47 1420.01 0.2977E+03 0.1159E+03 0.2915E+03 7 5.83 1676.63 972.74 1683.12 0.2901E+03 0.7739E+02 0.2499E+03 8 6.80 1955.75 1037.80 1904.41 0.2239E+03 0.5814E+02 0.2068E+03 9 7.77 2110.96 1088.21 2086.11 0.1376E+03 0.4689E+02 0.1691E+03 10 8.74 2222.70 1129.83 2235.03 0.1173E+03 0.3948E+02 0.1394E+03 11 9.71 2338.47 1165.43 2359.28 0.1153E+03 0.3422E+02 0.1181E+03 12 10.69 2447.37 1196.93 2467.40 0.1096E+03 0.3025E+02 0.1037E+03 13 11.66 2552.28 1224.73 2563.28 0.1051E+03 0.2721E+02 0.9477E+02 14 12.63 2651.26 1249.90 2652.43 0.9849E+02 0.2477E+02 0.8952E+02 15 13.60 2743.36 1272.93 2737.64 0.9179E+02 0.2277E+02 0.8643E+02 16 14.57 2829.33 1294.18 2820.43 0.8686E+02 0.2110E+02 0.8437E+02 17 15.54 2911.87 1313.94 2901.41 0.8337E+02 0.1968E+02 0.8258E+02 18 16.51 2991.07 1332.42 2980.56 0.7885E+02 0.1845E+02 0.8056E+02 19 17.49 3065.57 1349.96 3058.31 0.7197E+02 0.1738E+02 0.7802E+02 20 18.46 3131.48 1366.36 3132.53 0.6438E+02 0.1644E+02 0.7492E+02 21 19.43 3190.48 1381.90 3203.47 0.7606E+02 0.1562E+02 0.7126E+02 22 20.00 3238.94 1390.80 3243.42 -0.1860E+03 0.1516E+02 0.6889E+02 23 20.40 3088.50 1396.87 3088.50 -0.3761E+03 0.1487E+02 -0.3882E+03 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.41250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.35029862E+03 0.13828143E+05 -0.12668677E+06 0.35690645E+06 -0.41570783E+06 Rj0 = 20.0000 RKj = -0.45533706E+03



A.5 – 308


: :


Major parameters



1) 2)

pc =

2.6476"

------------------------------



Remark

Portugal


Ana M. Girao Coelho et al. (2007) EEP_10_2a


Tested by Test Id.

V -155

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 309


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1439E+03 0.1248E+03 0.2862E+03 2 1.00 143.88 127.04 164.81 0.1394E+03 0.1316E+03 0.1005E+03 3 2.00 278.82 269.02 261.93 0.1316E+03 0.1566E+03 0.1068E+03 4 3.00 407.01 449.88 387.28 0.1291E+03 0.2077E+03 0.1431E+03 5 4.00 537.04 650.02 542.60 0.1385E+03 0.1638E+03 0.1640E+03 6 5.00 684.04 773.78 708.41 0.1549E+03 0.9333E+02 0.1648E+03 7 6.00 846.88 850.00 867.57 0.1737E+03 0.6307E+02 0.1519E+03 8 7.00 1031.47 904.86 1010.20 0.1504E+03 0.4775E+02 0.1328E+03 9 8.00 1147.58 947.66 1132.77 0.1060E+03 0.3870E+02 0.1125E+03 10 10.00 1319.43 1013.55 1321.93 0.7731E+02 0.2840E+02 0.7874E+02 11 12.00 1456.82 1064.23 1456.57 0.5977E+02 0.2267E+02 0.5794E+02 12 14.00 1558.52 1105.64 1560.36 0.4838E+02 0.1901E+02 0.4710E+02 13 16.00 1650.35 1140.95 1648.57 0.4275E+02 0.1645E+02 0.4170E+02 14 18.00 1729.52 1171.86 1728.56 0.3674E+02 0.1455E+02 0.3848E+02 15 20.00 1797.32 1199.44 1802.75 0.3422E+02 0.1308E+02 0.3570E+02 16 22.00 1866.39 1224.39 1871.20 0.3207E+02 0.1191E+02 0.3268E+02 17 24.00 1925.61 1247.22 1933.24 0.2884E+02 0.1095E+02 0.2931E+02 18 26.00 1981.74 1268.30 1988.29 0.2796E+02 0.1015E+02 0.2572E+02 19 28.00 2037.46 1287.91 2036.12 0.2807E+02 0.9470E+01 0.2212E+02 20 30.00 2094.02 1306.25 2076.89 0.2374E+02 0.8885E+01 0.1869E+02 21 32.00 2132.42 1323.50 2111.08 0.1497E+02 0.8375E+01 0.1555E+02 22 34.00 2153.90 1339.79 2139.34 0.6718E+01 0.7927E+01 0.1277E+02 23 36.00 2159.29 1355.24 2162.41 -0.1031E+02 0.7529E+01 0.1037E+02 24 38.00 2112.66 1369.93 2137.85 -0.1698E+02 0.7174E+01 -0.1326E+02 25 40.00 2091.38 1383.96 2109.59 -0.1003E+02 0.6855E+01 -0.1495E+02 26 42.00 2072.52 1397.37 2078.26 -0.9426E+01 0.6566E+01 -0.1633E+02 27 45.00 2044.25 1416.48 2026.74 -0.9426E+01 0.6181E+01 -0.1793E+02 --------------------------------------------------------------------------------------------------




A.5 – 310


: :


Major parameters



1) 2)

pc =

2.6476"

------------------------------



Remark

Portugal


Ana M. Girao Coelho et al. (2007) EEP_10_2b


Tested by Test Id.

V -156

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

7

21

cc

pc

pic

pi pi

pit

pt

ct

28

35

42

49

56



14

beam

gt

63

li

70

nc

ni

nt

A.5 – 311


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1596E+03 0.1248E+03 0.2043E+03 2 1.00 159.57 127.04 162.09 0.1596E+03 0.1316E+03 0.1452E+03 3 2.00 319.13 269.02 314.07 0.1608E+03 0.1566E+03 0.1622E+03 4 3.00 481.07 449.88 485.80 0.1732E+03 0.2077E+03 0.1788E+03 5 4.00 665.61 650.02 666.06 0.1776E+03 0.1638E+03 0.1790E+03 6 5.00 836.32 773.78 839.18 0.1718E+03 0.9333E+02 0.1656E+03 7 6.00 1009.21 850.00 994.96 0.1510E+03 0.6307E+02 0.1454E+03 8 7.50 1186.59 927.27 1188.63 0.1050E+03 0.4274E+02 0.1133E+03 9 9.00 1324.32 983.27 1337.93 0.8556E+02 0.3267E+02 0.8703E+02 10 11.00 1478.74 1040.42 1486.91 0.7145E+02 0.2517E+02 0.6413E+02 11 13.00 1610.10 1085.84 1601.55 0.5859E+02 0.2066E+02 0.5185E+02 12 15.00 1713.11 1123.93 1698.11 0.4557E+02 0.1763E+02 0.4532E+02 13 17.00 1792.39 1156.88 1784.30 0.3764E+02 0.1544E+02 0.4105E+02 14 19.00 1863.67 1186.01 1862.59 0.3331E+02 0.1377E+02 0.3723E+02 15 21.00 1925.63 1212.21 1933.06 0.2927E+02 0.1247E+02 0.3319E+02 16 23.00 1980.76 1236.05 1995.19 0.2707E+02 0.1141E+02 0.2891E+02 17 25.00 2033.91 1257.96 2048.66 0.2582E+02 0.1053E+02 0.2457E+02 18 27.00 2084.04 1278.27 2093.58 0.2372E+02 0.9797E+01 0.2040E+02 19 29.00 2128.81 1297.22 2130.48 0.2091E+02 0.9167E+01 0.1658E+02 20 31.00 2167.68 1315.00 2160.20 0.1793E+02 0.8621E+01 0.1322E+02 21 33.00 2200.52 1331.75 2183.70 0.1350E+02 0.8144E+01 0.1036E+02 22 35.00 2221.68 1347.61 2201.97 0.7392E+01 0.7722E+01 0.7993E+01 23 37.00 2230.09 1362.67 2215.97 0.2052E+01 0.7347E+01 0.6078E+01 24 39.00 2229.88 1377.03 2226.55 -0.1026E+00 0.7011E+01 0.4558E+01 25 41.00 2229.68 1390.74 2234.43 -0.1027E+00 0.6707E+01 0.3373E+01 26 43.00 2229.47 1403.87 2240.22 -0.1027E+00 0.6432E+01 0.2464E+01 27 45.62 2229.20 1420.29 2245.48 -0.2624E+03 0.6107E+01 0.1599E+01 28 46.00 2115.04 1422.61 2115.04 -0.3004E+03 0.6063E+01 -0.3433E+03 --------------------------------------------------------------------------------------------------




A.5 – 312


: :



1.7421"

------------------------------


End-plate: 410x160x16 mm Failure mode: Nut stripping of bolt on tension side


1) 2)


Remark

Spain


J.M.Cabrero & E.Bayo (2007) A-M

Column : HEB160 Beam : IPE330 Plate thickness : 16 mm

Tested by Test Id.

V -157

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

5

15

cc

pc

pic

pi pi

pit

pt

ct

20

25

30

35

40



10

beam

gt

45

li

50

nc

ni

nt

A.5 – 313


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3147E+03 0.1407E+03 0.2676E+03 3 0.75 268.15 106.52 269.15 0.4433E+03 0.1448E+03 0.3989E+03 5 1.25 469.55 180.74 465.39 0.3623E+03 0.1529E+03 0.3793E+03 7 1.75 643.72 260.35 644.54 0.3344E+03 0.1667E+03 0.3354E+03 9 2.49 860.37 395.66 866.45 0.2612E+03 0.2025E+03 0.2652E+03 11 3.49 1082.36 624.31 1090.65 0.1932E+03 0.2343E+03 0.1873E+03 13 4.99 1318.59 870.74 1309.75 0.1153E+03 0.1056E+03 0.1119E+03 15 6.98 1472.80 1018.40 1475.05 0.5970E+02 0.5406E+02 0.6107E+02 17 8.98 1568.61 1106.94 1572.60 0.4024E+02 0.3694E+02 0.3984E+02 19 10.97 1641.99 1171.20 1643.03 0.3205E+02 0.2847E+02 0.3229E+02 21 12.97 1703.40 1222.64 1704.45 0.3117E+02 0.2335E+02 0.2948E+02 23 14.96 1766.47 1265.49 1761.04 0.2817E+02 0.1992E+02 0.2734E+02 25 16.96 1813.99 1302.72 1813.03 0.2283E+02 0.1744E+02 0.2452E+02 27 18.96 1856.62 1335.63 1858.66 0.2012E+02 0.1555E+02 0.2103E+02 29 20.95 1896.66 1365.06 1896.81 0.1802E+02 0.1408E+02 0.1730E+02 31 22.95 1926.97 1392.27 1927.77 0.1383E+02 0.1287E+02 0.1371E+02 33 24.94 1949.78 1416.85 1951.82 0.9576E+01 0.1189E+02 0.1054E+02 35 27.50 1974.16 1445.68 1974.41 -0.2775E+02 0.1085E+02 0.7251E+01 37 29.93 1793.81 1471.18 1801.17 -0.9184E+02 0.1003E+02 -0.7239E+02 --------------------------------------------------------------------------------------------------




A.5 – 314


: :



1.7421"


End-plate: 410x160x10 mm Failure mode: Nut stripping of bolt on tension side


1) 2)


Remark

Spain


J.M.Cabrero & E.Bayo (2007) B-M


Tested by Test Id.

V -158

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

13

39

52

65

78

91

cc

pc

pic

pi pi

pit

pt

ct

li

nc

ni

nt

104 117 130



26

beam

gt

A.5 – 315


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1568E+03 0.1155E+03 0.7766E+02 3 1.00 159.85 117.48 159.23 0.1748E+03 0.1217E+03 0.2061E+03 5 2.00 350.55 248.84 368.54 0.1984E+03 0.1449E+03 0.2001E+03 7 2.99 555.29 414.40 544.71 0.2097E+03 0.1918E+03 0.1532E+03 9 4.99 742.01 714.63 755.05 0.4640E+02 0.8673E+02 0.6426E+02 11 8.98 867.07 908.50 870.22 0.2554E+02 0.3032E+02 0.1457E+02 13 12.97 950.19 1003.53 937.86 0.1834E+02 0.1916E+02 0.2007E+02 15 16.96 1020.49 1069.22 1020.65 0.1544E+02 0.1431E+02 0.1999E+02 17 20.95 1087.58 1120.38 1091.11 0.1591E+02 0.1156E+02 0.1517E+02 19 24.94 1135.40 1162.68 1143.36 0.1201E+02 0.9764E+01 0.1142E+02 21 28.93 1183.79 1198.98 1185.51 0.1248E+02 0.8496E+01 0.1005E+02 23 32.92 1234.65 1230.90 1225.40 0.1168E+02 0.7548E+01 0.1007E+02 25 36.91 1275.81 1259.48 1266.25 0.9906E+01 0.6809E+01 0.1038E+02 27 40.91 1314.01 1285.49 1307.86 0.9356E+01 0.6214E+01 0.1034E+02 29 44.90 1349.50 1309.52 1348.16 0.8459E+01 0.5722E+01 0.9782E+01 31 48.89 1381.45 1331.49 1385.36 0.7500E+01 0.5314E+01 0.8808E+01 33 52.88 1409.81 1351.96 1418.14 0.6689E+01 0.4966E+01 0.7598E+01 35 56.87 1436.08 1371.15 1445.91 0.6156E+01 0.4666E+01 0.6323E+01 37 60.86 1459.05 1389.22 1468.68 0.5659E+01 0.4404E+01 0.5108E+01 39 64.85 1479.79 1406.20 1486.85 0.4821E+01 0.4174E+01 0.4026E+01 41 68.84 1498.33 1422.65 1501.03 0.3956E+01 0.3966E+01 0.3109E+01 43 72.83 1512.09 1437.99 1511.88 0.3430E+01 0.3784E+01 0.2360E+01 45 76.82 1525.38 1452.92 1520.06 0.3250E+01 0.3616E+01 0.1765E+01 47 80.81 1536.09 1466.88 1526.14 0.2033E+01 0.3468E+01 0.1304E+01 49 85.55 1545.30 1483.13 1531.31 -0.1086E+04 0.3305E+01 0.8978E+00 --------------------------------------------------------------------------------------------------




A.5 – 316


: :

G. Shi et al (2007) JD3


4.4094"



1) Plate size: 500x200x20 mm 2) Column flange thickness is taken the same as the end-plate thickness


Remark

China Fasteners: 10.9- -M20 7/8" Oversize holes Material : Q345 Fy = 54.04 ksi Fu = 77.89 ksi

Major parameters

Column : H300x250x8x12 Beam : H300x200x8x12 Plate thickness : 20 mm Stiffener thickness : 0.3937"

Tested by Test Id.

V -159

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

cc

pc

pic

pi pi

pit

pt

ct

88

Material : Q345 Fy = 54.04 ksi : Experimental : Polynominal : M. Exponential


22

beam

gt

99

li

110

nc

ni

nt

A.5 – 317


A3 = P3 =

2.040000 5

K = Q1 =

0.001545 0 Q2 =


( R : X 1/1000 radians )

-1

Q3 =


-1





A.5 – 318


: :



1) Plate size: 314x160x15 mm 2) Axial force of beam: 0 kN

pc =

1.4606"



Remark

Brazil Fasteners: 10.9- -M20 7/8" Oversize holes Material : S275 Fy = 53.58 ksi Fu = 73.02 ksi

Major parameters

L.R.O. Lima (2003) EE1


Tested by Test Id.

V -160

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

8

24

cc

pc

pic

pi pi

pit

pt

ct

32

40

48

56

64



16

beam

gt

72

li

80

nc

ni

nt

A.5 – 319


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1789E+03 0.6122E+02 0.2611E+03 3 0.71 128.23 43.84 136.55 0.1771E+03 0.6283E+02 0.1544E+03 5 1.23 220.56 77.33 214.78 0.1908E+03 0.6635E+02 0.1518E+03 7 1.75 308.06 113.31 297.44 0.1567E+03 0.7255E+02 0.1672E+03 9 2.27 386.84 153.44 388.59 0.1349E+03 0.8256E+02 0.1827E+03 11 2.79 470.93 199.91 486.20 0.2075E+03 0.9658E+02 0.1914E+03 13 3.30 578.64 251.99 584.26 0.1985E+03 0.1049E+03 0.1919E+03 15 3.82 686.98 303.44 682.56 0.1973E+03 0.8906E+02 0.1851E+03 17 4.34 782.32 343.38 775.79 0.1495E+03 0.6536E+02 0.1728E+03 19 5.38 860.72 395.43 859.12 0.5741E+02 0.3871E+02 0.6277E+02 21 7.45 922.29 453.63 917.21 0.2098E+02 0.2118E+02 -0.3705E+01 23 9.78 963.05 493.90 953.91 0.1466E+02 0.1433E+02 -0.3845E+01 25 12.63 1000.69 528.61 1001.88 0.7424E+01 0.1048E+02 0.9234E+01 27 15.14 1018.80 552.31 1019.41 0.9194E+01 0.8558E+01 0.5789E+01 29 18.09 1039.66 575.26 1035.95 0.5884E+01 0.7100E+01 0.5590E+01 31 21.05 1053.67 594.71 1052.21 0.4600E+01 0.6099E+01 0.5279E+01 33 24.01 1064.88 611.63 1066.56 0.3292E+01 0.5368E+01 0.4347E+01 35 26.96 1075.54 626.61 1077.74 0.2621E+01 0.4811E+01 0.3234E+01 37 29.92 1087.18 640.17 1085.83 0.3276E+01 0.4367E+01 0.2272E+01 39 32.88 1092.03 652.67 1091.47 0.2630E+01 0.4003E+01 0.1586E+01 41 35.83 1097.85 664.02 1095.46 0.1638E+01 0.3705E+01 0.1161E+01 43 38.79 1095.91 674.59 1098.52 -0.1638E+01 0.3452E+01 0.9296E+00 45 41.75 1098.82 684.47 1101.09 0.1973E+01 0.3235E+01 0.8243E+00 47 44.70 1103.67 693.73 1103.46 0.1966E+01 0.3047E+01 0.7921E+00 49 47.66 1109.49 702.43 1105.81 -0.8737E-01 0.2883E+01 0.7972E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.52816667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.17232495E+04 -0.16867090E+05 0.49449304E+05 -0.65614717E+05 0.43750804E+05 Rj0 = 4.3400 7.4500 9.7800 RKj = -0.76487548E+02 0.44698640E+02 0.32725634E+02



A.5 – 320


: :



1.4606"

------------------------------


1) Plate size: 314x160x15 mm 2) Axial force of beam: -135.94 kN (N / Ny = -10 %)


Remark


Major parameters



Tested by Test Id.

V -161

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

cc

pc

pic

pi pi

pit

pt

ct

88



22

beam

gt

99

li

110

nc

ni

nt

A.5 – 321


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1152E+03 0.6122E+02 0.1385E+03 3 1.05 118.87 65.53 122.83 0.1155E+03 0.6487E+02 0.1070E+03 5 2.50 290.61 173.05 281.11 0.1146E+03 0.8841E+02 0.1131E+03 7 3.95 437.14 314.71 446.83 0.1001E+03 0.8272E+02 0.1129E+03 9 5.40 587.29 396.35 601.81 0.9680E+02 0.3834E+02 0.9921E+02 11 6.85 745.28 440.06 731.63 0.1057E+03 0.2430E+02 0.7947E+02 13 8.30 848.61 470.20 832.40 0.4961E+02 0.1798E+02 0.5990E+02 15 11.21 948.32 512.67 961.11 0.2817E+02 0.1207E+02 0.3128E+02 17 14.11 1026.23 543.16 1028.58 0.1881E+02 0.9243E+01 0.1719E+02 19 17.01 1063.70 567.35 1068.94 0.1341E+02 0.7565E+01 0.1157E+02 21 20.64 1111.13 592.19 1105.85 0.1101E+02 0.6219E+01 0.9205E+01 23 25.00 1149.31 616.84 1142.85 0.7866E+01 0.5165E+01 0.7795E+01 25 29.35 1178.76 637.66 1173.48 0.5656E+01 0.4445E+01 0.6247E+01 27 33.71 1199.68 655.83 1197.13 0.3647E+01 0.3917E+01 0.4621E+01 29 38.07 1213.40 671.99 1214.08 0.1777E+01 0.3512E+01 0.3203E+01 31 42.42 1214.23 686.55 1225.53 0.3775E+00 0.3192E+01 0.2119E+01 33 46.78 1218.11 699.87 1232.99 0.2513E+01 0.2930E+01 0.1352E+01 35 51.13 1228.77 712.13 1237.69 0.1793E+01 0.2712E+01 0.8428E+00 37 55.49 1238.47 723.55 1240.59 0.1112E+01 0.2528E+01 0.5151E+00 39 59.84 1245.23 734.19 1242.35 0.9234E+00 0.2370E+01 0.3110E+00 41 64.20 1252.05 744.22 1243.41 0.2188E+01 0.2233E+01 0.1857E+00 43 68.55 1256.90 753.79 1244.04 0.2002E+01 0.2110E+01 0.1102E+00 45 72.18 1244.29 761.19 1244.37 -0.1204E+02 0.2022E+01 0.7100E-01 --------------------------------------------------------------------------------------------------




A.5 – 322


: :



1.4606"




Remark


Major parameters



Tested by Test Id.

V -162

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

10

30

40

50

60

70

cc

pc

pic

pi pi

pit

pt

ct

80



20

beam

gt

90

li

100

nc

ni

nt

A.5 – 323


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1263E+03 0.6122E+02 0.1463E+03 3 0.83 108.81 51.42 112.65 0.1367E+03 0.6345E+02 0.1286E+03 5 1.70 223.42 109.70 221.31 0.1118E+03 0.7181E+02 0.1218E+03 7 2.56 330.26 178.45 323.39 0.2087E+03 0.9007E+02 0.1152E+03 9 3.28 417.68 249.89 403.74 0.7955E+02 0.1050E+03 0.1076E+03 11 4.37 497.33 345.41 513.38 0.8483E+02 0.6414E+02 0.9309E+02 13 5.23 569.21 389.42 588.04 0.3406E+03 0.4123E+02 0.8051E+02 15 5.84 657.47 411.74 634.46 0.8177E+02 0.3261E+02 0.7171E+02 17 7.06 720.95 445.02 711.91 0.4654E+02 0.2310E+02 0.5569E+02 19 8.89 796.74 480.29 795.95 0.4725E+02 0.1630E+02 0.3737E+02 21 12.54 891.22 527.68 893.26 0.2236E+02 0.1056E+02 0.1926E+02 23 16.20 957.71 561.06 951.76 0.1466E+02 0.7962E+01 0.1377E+02 25 19.85 999.71 587.18 997.54 0.9998E+01 0.6464E+01 0.1147E+02 27 23.50 1032.83 608.86 1035.61 0.9580E+01 0.5480E+01 0.9365E+01 29 27.16 1064.92 627.57 1065.85 0.6488E+01 0.4778E+01 0.7163E+01 31 30.81 1083.45 644.00 1088.23 0.5061E+01 0.4251E+01 0.5154E+01 33 34.46 1101.97 658.74 1103.94 0.4809E+01 0.3840E+01 0.3527E+01 35 38.12 1113.69 672.17 1114.52 0.2142E+01 0.3508E+01 0.2318E+01 37 41.77 1125.42 684.46 1121.35 0.2686E+01 0.3235E+01 0.1479E+01 39 45.43 1130.34 695.87 1125.67 0.1619E+01 0.3006E+01 0.9202E+00 41 49.08 1138.18 706.47 1128.32 0.1081E+01 0.2810E+01 0.5619E+00 43 52.73 1137.28 716.41 1129.93 -0.1307E+01 0.2641E+01 0.3377E+00 45 56.39 1132.03 725.94 1130.89 -0.1251E+01 0.2491E+01 0.1999E+00 47 60.04 1125.77 734.72 1131.46 -0.1369E+01 0.2363E+01 0.1171E+00 49 63.70 1121.96 743.10 1131.79 -0.1312E+01 0.2247E+01 0.6786E-01 --------------------------------------------------------------------------------------------------




A.5 – 324


: :



1.4606"

------------------------------




Remark


Major parameters



Tested by Test Id.

V -163

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

cc

pc

pic

pi pi

pit

pt

ct

88



22

beam

gt

99

li

110

nc

ni

nt

A.5 – 325


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1081E+03 0.6122E+02 0.8946E+02 3 1.54 162.68 98.38 162.81 0.1040E+03 0.6966E+02 0.1138E+03 5 2.93 312.72 213.65 318.24 0.1124E+03 0.1003E+03 0.1072E+03 7 4.33 465.66 342.71 457.44 0.8737E+02 0.6575E+02 0.9090E+02 9 5.72 569.25 407.82 571.37 0.7765E+02 0.3398E+02 0.7316E+02 11 7.11 664.80 446.17 661.77 0.5790E+02 0.2283E+02 0.5738E+02 13 9.20 754.98 485.27 761.76 0.3546E+02 0.1555E+02 0.3950E+02 15 11.99 845.13 521.70 850.17 0.3102E+02 0.1113E+02 0.2544E+02 17 14.77 918.18 549.10 910.17 0.1828E+02 0.8791E+01 0.1856E+02 19 18.95 974.45 581.22 976.79 0.1321E+02 0.6773E+01 0.1395E+02 21 23.13 1031.18 606.82 1029.26 0.1198E+02 0.5564E+01 0.1125E+02 23 27.31 1071.93 628.28 1071.08 0.8320E+01 0.4753E+01 0.8775E+01 25 31.49 1101.91 646.87 1102.83 0.5595E+01 0.4167E+01 0.6463E+01 27 35.67 1123.35 663.32 1125.60 0.5574E+01 0.3723E+01 0.4501E+01 29 39.85 1138.97 678.12 1141.09 0.2082E+01 0.3373E+01 0.2987E+01 31 44.03 1151.42 691.60 1151.17 0.2857E+01 0.3089E+01 0.1900E+01 33 48.21 1160.50 704.01 1157.46 0.2237E+01 0.2854E+01 0.1163E+01 35 52.38 1168.35 715.49 1161.25 0.1659E+01 0.2657E+01 0.6880E+00 37 56.56 1168.43 726.23 1163.45 -0.5790E+00 0.2487E+01 0.3914E+00 39 60.74 1166.57 736.31 1164.68 -0.4452E+00 0.2340E+01 0.2135E+00 41 64.92 1160.83 745.95 1165.34 -0.9099E+00 0.2210E+01 0.1103E+00 43 69.10 1148.28 754.88 1165.67 -0.6951E+01 0.2097E+01 0.5272E-01 --------------------------------------------------------------------------------------------------




A.5 – 326


: :



1.4606"

------------------------------




Remark


Major parameters



Tested by Test Id.

V -164

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

cc

pc

pic

pi pi

pit

pt

ct

88



22

beam

gt

99

li

110

nc

ni

nt

A.5 – 327


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1381E+03 0.6122E+02 0.1385E+03 3 1.45 198.72 92.16 199.25 0.1370E+03 0.6859E+02 0.1320E+03 5 2.87 367.88 207.67 372.82 0.1043E+03 0.9874E+02 0.1115E+03 7 4.28 513.99 339.37 514.58 0.9315E+02 0.6777E+02 0.8980E+02 9 5.69 627.27 406.79 627.42 0.7074E+02 0.3435E+02 0.7085E+02 11 7.82 758.10 461.18 753.87 0.4856E+02 0.1964E+02 0.4926E+02 13 10.65 865.46 505.70 865.64 0.3276E+02 0.1285E+02 0.3144E+02 15 14.89 965.63 550.17 967.11 0.1867E+02 0.8713E+01 0.1826E+02 17 19.14 1029.81 582.50 1030.29 0.1232E+02 0.6705E+01 0.1213E+02 19 23.38 1074.88 608.20 1073.68 0.9285E+01 0.5507E+01 0.8586E+01 21 27.63 1104.87 629.80 1104.64 0.5059E+01 0.4702E+01 0.6113E+01 23 31.87 1125.23 648.44 1126.49 0.4781E+01 0.4122E+01 0.4286E+01 25 36.11 1141.52 664.94 1141.66 0.2466E+01 0.3682E+01 0.2938E+01 27 40.36 1152.58 679.83 1151.97 0.2997E+01 0.3335E+01 0.1969E+01 29 44.60 1157.26 693.35 1158.80 -0.2866E+00 0.3054E+01 0.1297E+01 31 48.85 1166.34 705.83 1163.27 0.2157E+01 0.2822E+01 0.8400E+00 33 53.09 1161.72 717.36 1166.15 0.3467E+00 0.2626E+01 0.5381E+00 35 57.34 1168.45 728.16 1167.99 0.1374E+00 0.2458E+01 0.3410E+00 37 61.58 1169.09 738.26 1169.15 0.4775E+00 0.2313E+01 0.2147E+00 39 65.83 1169.38 747.95 1169.88 0.2200E-01 0.2184E+01 0.1343E+00 41 70.07 1171.61 756.90 1170.33 0.4775E+00 0.2073E+01 0.8370E-01 --------------------------------------------------------------------------------------------------




A.5 – 328


: :



1.4606"

------------------------------


1) Plate size: 314x160x15 mm 2) Axial force of beam: 127.2 kN (N / Ny = +10 %)


Remark


Major parameters



Tested by Test Id.

V -165

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

cc

pc

pic

pi pi

pit

pt

ct

88



22

beam

gt

99

li

110

nc

ni

nt

A.5 – 329


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3





A.5 – 330


: :



1.4606"

------------------------------


1) Plate size: 314x160x15 mm 2) Axial force of beam: 257.9 kN (N / Ny = +20 %)


Remark


Major parameters



Tested by Test Id.

V -166

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

cc

pc

pic

pi pi

pit

pt

ct

96



24

beam

gt

nc

ni

108 120

li

nt

A.5 – 331


R tf A3 P3


( R : X 1/1000 radians )

-1

Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.6584E+02 0.6122E+02 0.6257E+02 3 1.47 93.75 93.54 86.20 0.5451E+02 0.6882E+02 0.5774E+02 5 2.98 170.85 218.68 175.83 0.5820E+02 0.1014E+03 0.6112E+02 7 4.49 264.31 352.75 269.79 0.6073E+02 0.5984E+02 0.6276E+02 9 6.00 360.54 416.88 363.65 0.7652E+02 0.3090E+02 0.6104E+02 11 7.51 467.41 454.91 452.86 0.5280E+02 0.2091E+02 0.5679E+02 13 9.02 536.06 482.39 534.49 0.3979E+02 0.1598E+02 0.5120E+02 15 10.53 599.86 504.13 607.26 0.4804E+02 0.1304E+02 0.4518E+02 17 12.04 669.06 522.25 671.04 0.4001E+02 0.1108E+02 0.3934E+02 19 15.06 770.90 551.63 774.03 0.3166E+02 0.8607E+01 0.2929E+02 21 18.08 844.20 575.19 850.54 0.2325E+02 0.7104E+01 0.2179E+02 23 21.10 914.56 595.01 907.85 0.1552E+02 0.6085E+01 0.1648E+02 25 25.63 962.08 620.06 969.80 0.1227E+02 0.5045E+01 0.1131E+02 27 30.16 1018.32 641.21 1013.24 0.8952E+01 0.4335E+01 0.8101E+01 29 34.69 1047.17 659.62 1044.75 0.5134E+01 0.3817E+01 0.5938E+01 31 39.22 1064.88 675.98 1067.93 0.3536E+01 0.3421E+01 0.4374E+01 33 43.75 1070.65 690.74 1084.96 0.2427E+01 0.3106E+01 0.3201E+01 35 48.28 1095.66 704.21 1097.36 0.1748E+01 0.2851E+01 0.2314E+01 37 52.81 1103.67 716.63 1106.26 0.2971E+01 0.2638E+01 0.1650E+01 39 57.35 1107.24 728.18 1112.58 0.1232E+01 0.2458E+01 0.1159E+01 41 61.88 1110.26 738.96 1116.98 0.1793E+01 0.2303E+01 0.8037E+00 43 66.41 1128.88 749.08 1120.01 0.1185E+01 0.2169E+01 0.5508E+00 45 70.94 1140.52 758.77 1122.08 0.1790E+01 0.2050E+01 0.3735E+00 47 74.71 1097.85 766.23 1123.28 -0.2569E+02 0.1964E+01 0.2684E+00 --------------------------------------------------------------------------------------------------




A.5 – 332


: :


1) 2)

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------


fy = 41.3 ksi, fu = 66.9 ksi for beam. fy = 51.1 ksi, fu = 77.3 ksi for column.

pt = 2.5000" gt = 3.5000" nt = 2 X 1

Actual strength Actual strength

0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters

J.R.Ostrander (1970) TEST 1


Tested by Test Id.

VI -

1

0

70

140

210

280

350

420

490

560

630

700

tp

column

Moment ( kip-inch )

Connection type : Flush end-plate connections Mode : All bolted without column stiffener

0

9

27

36

45

54

63

pc cc

li

ct pt

72


gc


18

beam

gt

81

lp

90

nc

ni

nt

A.6 – 1


R tf A3 P3


Q3 =


-3





A.6 – 2


: :


1) 2)

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 3.5000" nt = 2 X 1


0.5000" 0.5000" 0.3750"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

2

0

60

120

180

240

300

360

420

480

540

600

tp

column

Moment ( kip-inch )


0

8

24

32

40

48

56

pc cc

li

ct pt

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 3


R tf A3 P3


Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.50000000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 1 AI = 0.15702656E+02 0.27165523E+01 0.28144999E+02 0.10355672E+04 -0.23692699E+04 Rj0 = 16.4800 RKj = 0.16923591E+01



A.6 – 4


: :


1) 2)

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 3.5000" nt = 2 X 1


0.5000" 0.5000" 0.2500"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

3

0

35

70

105

140

175

210

245

280

315

350

tp

column

Moment ( kip-inch )


0

6

18

24

30

36

42

pc cc

li

ct pt

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 5


R tf A3 P3


Q3 =


-3





A.6 – 6


: :


1) 2)

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 3.5000" nt = 2 X 1


0.5000" 0.5000" 0.7500"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

4

0

75

150

225

300

375

450

525

600

675

750

tp

column

Moment ( kip-inch )


0

9

27

36

45

54

63

pc cc

li

ct pt

72


gc


18

beam

gt

81

lp

90

nc

ni

nt

A.6 – 7


R tf A3 P3


Q3 =


-3





A.6 – 8


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 4.0000" nt = 2 X 1


0.5000" 0.5000" 0.3750"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

5

0

80

160

240

320

400

480

560

640

720

800

tp

column

Moment ( kip-inch )


0

9

27

36

45

54

63

pc cc

li

ct pt

72


gc


18

beam

gt

81

lp

90

nc

ni

nt

A.6 – 9


R tf A3 P3


Q3 =


-3





A.6 – 10


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 4.0000" nt = 2 X 1


0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

6

0

100

200

300

400

500

600

700

800

900

1000

tp

column

Moment ( kip-inch )


0

8

24

pc cc

li

ct pt

32

40

48

56

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 11


R tf A3 P3


Q3 =


-3





A.6 – 12


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 4.0000" nt = 2 X 1


0.5000" 0.5000" 0.6250"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

7

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 13


R tf A3 P3


Q3 =


-3





A.6 – 14


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------


fy = 58.0 ksi, fu = 78.8 ksi for beam.

pt = 2.5000" gt = 4.0000" nt = 2 X 1

Actual strength

0.5000" 0.5000" 0.3750"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

8

0

70

140

210

280

350

420

490

560

630

700

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

pc cc

li

ct pt

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.6 – 15


R tf A3 P3


Q3 =


-3





A.6 – 16


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 4.0000" nt = 2 X 1

Actual strength

0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI -

9

0

85

170

255

340

425

510

595

680

765

850

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

pc cc

li

ct pt

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.6 – 17


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7231E+02 0.7493E+01 0.6349E+02 3 0.87 62.66 6.58 60.76 0.7230E+02 0.7792E+01 0.7297E+02 5 1.80 125.33 14.31 126.90 0.6267E+02 0.8975E+01 0.6726E+02 7 2.80 188.00 24.59 188.69 0.5685E+02 0.1186E+02 0.5611E+02 9 4.07 250.67 39.68 251.12 0.4947E+02 0.9432E+01 0.4298E+02 11 5.80 313.33 50.23 314.16 0.2848E+02 0.4048E+01 0.3085E+02 13 8.00 376.00 56.88 371.94 0.2400E+02 0.2322E+01 0.2260E+02 15 11.53 435.33 63.22 438.46 0.1679E+02 0.1427E+01 0.1568E+02 17 15.70 490.50 68.18 491.80 0.1062E+02 0.1007E+01 0.1026E+02 19 21.95 540.00 73.45 540.34 0.6234E+01 0.7164E+00 0.5996E+01 21 29.27 578.00 78.00 578.13 0.4038E+01 0.5455E+00 0.4663E+01 23 36.20 606.00 81.43 608.38 0.3995E+01 0.4497E+00 0.4033E+01 25 43.80 636.00 84.57 635.46 0.3947E+01 0.3798E+00 0.3051E+01 27 51.52 655.80 87.29 654.88 0.1224E+01 0.3298E+00 0.2001E+01 29 59.36 665.40 89.73 667.12 0.1224E+01 0.2921E+00 0.1171E+01 31 67.20 675.00 91.90 674.02 -0.8264E-01 0.2629E+00 0.6350E+00 33 73.20 668.50 93.42 668.58 -0.1083E+01 0.2446E+00 -0.1023E+01 35 79.20 662.00 94.84 661.93 -0.1083E+01 0.2290E+00 -0.1181E+01 --------------------------------------------------------------------------------------------------




A.6 – 18


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 4.0000" nt = 2 X 1

Actual strength

0.5000" 0.5000" 0.6250"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI - 10

0

80

160

240

320

400

480

560

640

720

800

tp

column

Moment ( kip-inch )


0

7

21

28

35

42

49

pc cc

li

ct pt

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 19


R tf A3 P3


Q3 =


-3





A.6 – 20


: :


1) 2)

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



pt = 2.5000" gt = 4.0000" nt = 2 X 1


0.5000" 0.5000" 0.6250"


Remark

ct = cc = tp =


Major parameters



Tested by Test Id.

VI - 11

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

4

12

pc cc

li

ct pt

16

20

24

28

32


gc


8

beam

gt

36

lp

40

nc

ni

nt

A.6 – 21


R tf A3 P3


Q3 =


-3





A.6 – 22


: :



pt = 2.5000" gt = 3.5000" nt = 2 X 1

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------


1) 3 x 7 1/8 x 3/8 column web stiffeners used, fy = 50.5 ksi, fu = 72.5 ksi. 2) fy = 41.3, fu = 66.9 ksi for beam, fy = 51.1, fu = 77.3 ksi for column.

0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 12

0

75

150

225

300

375

450

525

600

675

750

tp

column

Moment ( kip-inch )

Connection type : Flush end-plate connections Mode : All bolted with column stiffener

0

8

24

32

40

48

56

pc cc

li

ct pt

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 23


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.074964 0 Q2 =

R = Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) -1

Q3 =


-1





A.6 – 24


: :



pt = 2.5000" gt = 3.5000" nt = 2 X 1

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 13

0

85

170

255

340

425

510

595

680

765

850

tp

column

Moment ( kip-inch )


0

16

48

64

80

96

pc cc

li

ct pt

lp

nc

ni

nt

112 128 144 160


gc


32

beam

gt

A.6 – 25


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.074964 0 Q2 =


Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.9401E+02 0.7452E+01 0.1031E+03 3 0.50 47.00 3.70 50.68 0.9400E+02 0.7263E+01 0.9898E+02 5 1.00 94.00 7.18 98.51 0.9400E+02 0.6576E+01 0.9204E+02 7 1.50 141.00 10.20 142.48 0.9401E+02 0.5452E+01 0.8368E+02 9 2.00 188.00 12.63 182.12 0.8281E+02 0.4325E+01 0.7487E+02 11 2.70 235.00 15.23 230.29 0.6061E+02 0.3169E+01 0.6287E+02 13 3.60 282.00 17.64 280.56 0.4663E+02 0.2286E+01 0.4926E+02 15 4.80 329.00 19.96 330.75 0.3497E+02 0.1649E+01 0.3519E+02 17 6.40 376.00 22.21 376.48 0.2507E+02 0.1203E+01 0.2309E+02 19 9.00 423.00 24.81 422.55 0.1567E+02 0.8432E+00 0.1389E+02 21 12.90 470.00 27.54 466.40 0.1027E+02 0.5908E+00 0.9410E+01 23 19.30 517.00 30.65 513.30 0.5682E+01 0.4043E+00 0.5327E+01 25 27.63 546.33 33.49 550.28 0.3520E+01 0.2922E+00 0.2883E+01 27 36.60 570.25 35.80 569.90 0.1927E+01 0.2280E+00 0.1823E+01 29 46.20 588.75 37.77 586.92 0.1927E+01 0.1863E+00 0.1766E+01 31 55.64 604.54 39.39 603.41 0.1412E+01 0.1589E+00 0.1708E+01 33 64.91 617.63 40.77 618.61 0.1412E+01 0.1393E+00 0.1562E+01 35 74.18 630.72 41.99 632.38 0.1412E+01 0.1245E+00 0.1414E+01 37 83.45 643.81 43.09 644.96 0.1412E+01 0.1127E+00 0.1306E+01 39 92.73 656.91 44.09 656.73 0.1412E+01 0.1032E+00 0.1239E+01 41 102.00 670.00 45.02 668.02 0.1412E+01 0.9522E-01 0.1201E+01 --------------------------------------------------------------------------------------------------




A.6 – 26


: :



pt = 2.5000" gt = 3.5000" nt = 2 X 1

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.3750"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 14

0

65

130

195

260

325

390

455

520

585

650

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

pc cc

li

ct pt

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.6 – 27


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.089088 0 Q2 =


Q3 =


-1





A.6 – 28


: :



pt = 2.5000" gt = 3.5000" nt = 2 X 1

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.2500"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 15

0

40

80

120

160

200

240

280

320

360

400

tp

column

Moment ( kip-inch )


0

8

24

32

40

48

56

pc cc

li

ct pt

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 29


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.113625 0 Q2 =


Q3 =


-1





A.6 – 30


: :



pt = 2.5000" gt = 3.5000" nt = 2 X 1

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.2500"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 16

0

40

80

120

160

200

240

280

320

360

400

tp

column

Moment ( kip-inch )


0

7

21

28

35

42

49

pc cc

li

ct pt

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 31


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.113625 0 Q2 =


Q3 =


-1





A.6 – 32


: :



pt = 2.5000" gt = 3.5000" nt = 2 X 1

li = 5.0000" gc = 3.5000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.7500"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 17

0

90

180

270

360

450

540

630

720

810

900

tp

column

Moment ( kip-inch )


0

8

24

32

40

48

56

pc cc

li

ct pt

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 33


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.058776 0 Q2 =


Q3 =


-1





A.6 – 34


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------


1) 4 x 7 x 1/4 column web stiffeners used, fy = 52.5 ksi, fu = 75.3 ksi. 2) fy = 58.0, fu = 78.8 ksi for beam, fy = 42.0, fu = 71.6 ksi for column.

0.5000" 0.5000" 0.3750"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 18

0

90

180

270

360

450

540

630

720

810

900

tp

column

Moment ( kip-inch )


0

8

24

32

40

48

56

pc cc

li

ct pt

64


gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 35


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.064660 0 Q2 =


Q3 =


-1





A.6 – 36


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 19

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

4

12

16

20

24

28

gc


8


beam

gt

32

pc cc

li

ct pt

36

lp

40

nc

ni

nt

A.6 – 37


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.054409 0 Q2 =


Q3 =


-1





A.6 – 38


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.6250"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 20

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

5

15

pc cc

li

ct pt

20

25

30

35

40


gc


10

beam

gt

45

lp

50

nc

ni

nt

A.6 – 39


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.047591 0 Q2 =


Q3 =


-1





A.6 – 40


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------


1) 3 x 7 1/8 x 1/4 column web stiffeners used, fy = 41.4 ksi, fu = 57.0 ksi. 2) fy = 58.0, fu = 78.8 ksi for beam.

0.5000" 0.5000" 0.3750"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 21

0

80

160

240

320

400

480

560

640

720

800

tp

column

Moment ( kip-inch )


0

11

33

44

55

66

77

pc cc

li

ct pt

88


gc


22

beam

gt

99

lp

110

nc

ni

nt

A.6 – 41


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.064660 0 Q2 =


Q3 =


-1





A.6 – 42


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.5000"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 22

0

100

200

300

400

500

600

700

800

900

1000

tp

column

Moment ( kip-inch )


0

10

30

40

50

60

70

pc cc

li

ct pt

80


gc


20

beam

gt

90

lp

100

nc

ni

nt

A.6 – 43


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.054409 0 Q2 =


Q3 =


-1





A.6 – 44


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.6250"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 23

0

95

190

285

380

475

570

665

760

855

950

tp

column

Moment ( kip-inch )


0

7

21

28

35

42

49

pc cc

li

ct pt

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 45


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.047591 0 Q2 =


Q3 =


-1





A.6 – 46


: :



pt = 2.5000" gt = 4.0000" nt = 2 X 1

li = 7.0000" gc = 4.0000" nc = 2 X 1

pc =

2.5000"

------------------------------



0.5000" 0.5000" 0.6250"


Remark

ct = cc = tp =


Major parameters


Tested by Test Id.

VI - 24

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

3

9

pc cc

li

ct pt

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.6 – 47


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.047591 0 Q2 =


Q3 =


-1

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3133E+03 0.1174E+02 0.2733E+03 3 0.30 94.00 3.51 104.18 0.4074E+03 0.1164E+02 0.3798E+03 5 0.50 188.00 5.82 178.82 0.4074E+03 0.1144E+02 0.3605E+03 7 0.80 282.00 9.18 277.68 0.2797E+03 0.1090E+02 0.2961E+03 9 1.20 376.00 13.32 379.15 0.2141E+03 0.9698E+01 0.2154E+03 11 1.70 470.00 17.70 469.56 0.1656E+03 0.7844E+01 0.1527E+03 13 2.40 564.00 22.39 559.65 0.1177E+03 0.5673E+01 0.1100E+03 15 3.40 658.00 27.05 651.77 0.7809E+02 0.3845E+01 0.7639E+02 17 5.20 747.00 32.44 751.27 0.4378E+02 0.2376E+01 0.3903E+02 19 6.40 795.00 34.98 791.26 0.3416E+02 0.1895E+01 0.2919E+02 21 8.10 839.00 37.82 836.50 0.2443E+02 0.1479E+01 0.2489E+02 23 9.57 873.00 39.81 871.26 0.2318E+02 0.1249E+01 0.2237E+02 25 11.23 902.67 41.73 905.22 0.1357E+02 0.1065E+01 0.1817E+02 27 13.10 928.00 43.57 934.09 0.1492E+02 0.9169E+00 0.1279E+02 29 14.60 952.00 44.87 950.33 0.1043E+02 0.8267E+00 0.8974E+01 31 16.00 959.33 45.99 960.83 0.5240E+01 0.7576E+00 0.6163E+01 33 17.45 970.50 47.05 968.13 0.1000E+02 0.6986E+00 0.4030E+01 35 19.05 966.50 48.12 963.86 -0.1353E+02 0.6441E+00 -0.8567E+01 --------------------------------------------------------------------------------------------------




A.6 – 48


: :


1) 2)

= = = =

pt = 1.9685" pit= 1.9685" gi = 2.9921" nt = 2 X 1

li pi gc ni

= 5.9055" = 0.0000" = 2.9921" = 2 X 1

------------------------------


1

2.1260" 3.9370"

nc = 2 X

pc = pic=

Suddenly failed at 0,01 radian and 407 kip-in (A) Premature weld failure (B) Minor axis connection

0.1969" 0.2362" 2.9921" 0.4724"

Major parameters


Remark

ct cc gt tp

United Kingdom

Fasteners: 10.9- -M16 23/32" Oversize holes Material : 43A Fy = -ksi Fu = -ksi



Tested by Test Id.

VI - 25

0

50

100

150

200

250

300

350

400

450

500

tp

column

Moment ( kip-inch )


0

2

6

8

12

14

pc cc

li

ct pt

16


10

Material : : :

gc


4

beam

gt

18

lp

20

nc

ni

nt

A.6 – 49


R tf A3 P3


Q3 =


-3





A.6 – 50


: :


1) 2)

= = = =

pt = 1.9685" pit= 1.9685" gi = 2.9921" nt = 2 X 1

li pi gc ni

= 5.9055" = 0.0000" = 2.9921" = 2 X 1 1

2.1260" 3.9370"

nc = 2 X

pc = pic=

------------------------------


The bolt stripping was the cause of failure Minor axis connection

0.1969" 0.2362" 2.9921" 0.4724"

Major parameters


Remark

ct cc gt tp

United Kingdom


J.B.Davison et al (1987) JT/11B


Tested by Test Id.

VI - 26

0

55

110

165

220

275

330

385

440

495

550

tp

column

Moment ( kip-inch )


0

3

9

12

18

21

pc cc

li

ct pt

24


15

Material : : :

gc


6

beam

gt

27

lp

30

nc

ni

nt

A.6 – 51


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.3833E+03 0.2809E+01 0.1571E+03 3 0.10 36.87 0.27 27.33 0.3837E+03 0.2810E+01 0.3802E+03 5 0.19 73.75 0.54 68.54 0.3837E+03 0.2814E+01 0.4598E+03 7 0.29 110.62 0.81 113.24 0.3833E+03 0.2821E+01 0.4601E+03 9 0.38 147.49 1.08 155.75 0.3833E+03 0.2830E+01 0.4202E+03 11 0.48 184.37 1.36 193.52 0.3837E+03 0.2842E+01 0.3635E+03 13 0.58 221.24 1.63 225.56 0.3833E+03 0.2857E+01 0.3034E+03 15 0.67 258.11 1.90 251.98 0.3837E+03 0.2875E+01 0.2469E+03 17 0.79 294.98 2.24 277.12 0.2183E+03 0.2901E+01 0.1881E+03 19 1.25 320.79 3.61 328.68 0.3836E+02 0.3052E+01 0.6031E+02 21 1.73 342.93 5.13 347.71 0.5757E+02 0.3315E+01 0.2760E+02 23 2.40 368.73 7.56 363.20 0.2170E+02 0.3940E+01 0.2038E+02 25 3.37 381.02 11.88 380.32 0.1279E+02 0.4788E+01 0.1550E+02 27 4.49 395.77 16.18 396.31 0.1342E+02 0.2750E+01 0.1371E+02 29 5.77 412.98 18.79 413.73 0.1232E+02 0.1533E+01 0.1324E+02 31 6.73 424.04 20.05 425.74 0.1214E+02 0.1149E+01 0.1153E+02 33 7.69 436.33 21.04 435.64 0.1278E+02 0.9244E+00 0.8465E+01 35 8.65 443.95 21.86 442.54 0.3067E+01 0.7769E+00 0.5926E+01 37 9.62 446.90 22.55 447.18 0.1533E+01 0.6726E+00 0.3810E+01 39 10.58 446.90 23.16 450.05 -0.3961E+01 0.5949E+00 0.2243E+01 41 11.56 439.03 23.71 436.96 -0.8008E+01 0.5335E+00 -0.1388E+02 43 12.52 425.27 24.21 423.26 -0.2091E+02 0.4850E+00 -0.1457E+02 45 13.46 405.60 24.64 409.35 -0.2091E+02 0.4466E+00 -0.1498E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12420000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.74614207E+03 0.55949559E+04 -0.19360171E+05 0.38588641E+05 -0.38080533E+05 Rj0 = 7.6900 10.5800 RKj = -0.55719545E+00 -0.15033936E+02



A.6 – 52


: :


1) 2)

= = = =

pt = 1.9685" pit= 1.9685" gi = 2.9921" nt = 2 X 1

li pi gc ni

= 5.9055" = 0.0000" = 2.9921" = 2 X 1 1

2.1260" 3.9370"

nc = 2 X

pc = pic=

------------------------------


The bolt stripping was the failure Minor axis connection

0.1969" 0.2362" 2.9921" 0.4724"

Major parameters


Remark

ct cc gt tp

United Kingdom




Tested by Test Id.

VI - 27

0

30

60

90

120

150

180

210

240

270

300

tp

column

Moment ( kip-inch )


0

4

12

16

24

28

pc cc

li

ct pt

32


20

Material : : :

gc


8

beam

gt

36

lp

40

nc

ni

nt

A.6 – 53


R tf A3 P3


Q3 =


-3





A.6 – 54


: :


1) 2)

= = = =

pt = 1.7385" pit= 2.3622" gi = 3.1496" nt = 2 X 1

li pi gc ni

= 6.6930" = 0.0000" = 3.1496" = 2 X 1 1

1.7385" 4.3308"

nc = 2 X

pc = pic=

VI - 28


tp

column

------------------------------


Slight increase in bolt force in top bolt row before separation Bolt preloaded to aproximatly 39 kip

0.4269" 0.4269" 3.1496" 0.3750"

Major parameters


Remark

ct cc gt tp

Canada

Fasteners: A325- -7/8"D 7/8" Oversize holes Material : -Fy = 41.30 ksi Fu = -ksi

J.Phillips & J.A.Packer (1981) BM1


Tested by Test Id.


0

150

300

450

600

750

900

1050

1200

1350

1500

0

7

beam

21

28

35

42


14

pc cc

li

ct pt

56


gc

gt

63

lp

70

nc

ni

nt

A.6 – 55


Moment ( kip-inch )

( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.114754 0 Q2 =


Q3 =


-1





A.6 – 56


: :


1) 2)

= = = =

pt = 1.7385" pit= 2.3622" gi = 3.1496" nt = 2 X 1

li pi gc ni

= 6.6930" = 0.0000" = 3.1496" = 2 X 1 1

1.7385" 4.3308"

nc = 2 X

pc = pic=

------------------------------


Slight increase in bolt force in top bolt row before sepration Bolt preloaded upto aproximately 39 kip

0.4269" 0.4269" 3.1496" 0.6250"

Major parameters


Remark

ct cc gt tp

Canada




Tested by Test Id.

VI - 29

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 57


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.084462 0 Q2 =


Q3 =


-1





A.6 – 58


: :


1) 2)

= = = =

pt = 1.7385" pit= 2.3622" gi = 3.1496" nt = 2 X 1

li pi gc ni

= 6.6930" = 0.0000" = 3.1496" = 2 X 1 1

1.7385" 4.3308"

nc = 2 X

pc = pic=

------------------------------


(A) Bolts were preloaded (B) Failure occured due to bolt fracture (A) Clear separation occured (B) End plate collapsed

0.4269" 0.4269" 3.1496" 0.7500"

Major parameters


Remark

ct cc gt tp

Canada




Tested by Test Id.

VI - 30

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 59


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.075709 0 Q2 =


Q3 =


-1





A.6 – 60


: :


1) 2)

= = = =

pt = 1.7385" pit= 2.3622" gi = 3.1496" nt = 2 X 1

li pi gc ni

= 6.6930" = 0.0000" = 3.1496" = 2 X 1 1

1.7385" 4.3308"

nc = 2 X

pc = pic=

------------------------------


(A) Bolts were preloaded (B) Failure due to bolt fracture (A) Clear separation occured (B) End plate collapsed

0.4269" 0.4269" 3.1496" 0.8750"

Major parameters


Remark

ct cc gt tp

Canada




Tested by Test Id.

VI - 31

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 61


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.069021 0 Q2 =


Q3 =


-1





A.6 – 62


: :


1) 2)

= = = =

pt = 1.7385" pit= 2.3622" gi = 3.1496" nt = 2 X 1

li pi gc ni

= 6.6930" = 0.0000" = 3.1496" = 2 X 1

------------------------------


1

1.7385" 4.3308"

nc = 2 X

pc = pic=

(A) Bolts were preloaded (B) Failure due bolt fracture (A) Clear separation occured (B) End plate yielded

0.4269" 0.4269" 3.1496" 1.0000"

Major parameters


Remark

ct cc gt tp

Canada




Tested by Test Id.

VI - 32

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

4

12

pc cc

li

ct pt

16

20

24

28

32


gc


8

beam

gt

36

lp

40

nc

ni

nt

A.6 – 63


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.063707 0 Q2 =


Q3 =


-1





A.6 – 64


: :


1) 2)

0.0000" 0.0000" 0.4724"

pt = 2.3622" gt = 4.1339" nt = 2 X 1

pc =

2.3622"

------------------------------


li = 7.0866" gc = 4.1339" nc = 2 X 1

Major parameters


Remark

ct = cc = tp =

Italy

Fasteners: G8.8- -M20 7/8" Oversize holes Material : -Fy = 45.40 ksi Fu = 66.57 ksi

C.Bernuzzi et al. (1996) FPC/M

Column : -Beam : IPE300 Plate thickness : 12 mm

Tested by Test Id.

VI - 33

0

80

160

240

320

400

480

560

640

720

800

tp

column

Moment ( kip-inch )


0

12

36

48

60

72

84

pc cc

li

ct pt

96


gc


24

beam

gt

nc

ni

108 120

lp

nt

A.6 – 65


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4593E+03 0.8528E+01 0.5654E+03 3 0.20 91.86 1.71 97.84 0.4593E+03 0.8545E+01 0.4186E+03 5 0.40 183.72 3.42 169.45 0.3746E+03 0.8598E+01 0.3021E+03 7 1.02 267.34 8.86 278.81 0.8199E+02 0.9006E+01 0.8017E+02 9 2.04 322.18 18.81 318.65 0.3966E+02 0.1081E+02 0.2913E+02 11 4.14 375.12 45.90 378.48 0.2167E+02 0.1028E+02 0.4384E+02 13 8.27 411.30 65.42 416.34 0.6757E+01 0.2517E+01 0.8908E+01 15 12.41 442.68 73.32 445.21 0.6465E+01 0.1489E+01 0.7602E+01 17 16.54 461.97 78.53 461.96 0.5811E+01 0.1085E+01 0.2862E+01 19 20.68 479.43 82.53 478.13 0.3877E+01 0.8646E+00 0.5189E+01 21 24.81 498.86 85.79 503.83 0.6001E+01 0.7248E+00 0.6991E+01 23 28.95 519.22 88.58 516.78 0.1443E+01 0.6272E+00 0.3231E+01 25 33.08 522.12 91.01 529.69 0.3131E+01 0.5551E+00 0.2977E+01 27 37.22 537.23 93.19 541.34 0.3373E+01 0.4992E+00 0.2672E+01 29 41.35 557.35 95.16 552.01 0.2565E+01 0.4547E+00 0.2526E+01 31 45.49 557.11 96.98 562.45 0.1353E+01 0.4178E+00 0.2536E+01 33 49.62 577.38 98.64 573.12 0.4110E+01 0.3875E+00 0.2641E+01 35 53.76 591.92 100.19 584.34 0.2921E+01 0.3617E+00 0.2782E+01 37 57.89 593.81 101.63 596.12 0.3842E+00 0.3395E+00 0.2919E+01 39 62.03 604.54 103.00 608.45 0.4113E+01 0.3201E+00 0.3036E+01 41 66.16 622.81 104.27 621.19 0.4162E+01 0.3032E+00 0.3127E+01 43 70.30 633.78 105.51 634.28 0.9123E+00 0.2878E+00 0.3195E+01 45 74.43 631.38 106.66 630.37 -0.1444E+01 0.2744E+00 -0.9253E+00 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.66250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.34684645E+04 -0.20648853E+05 0.57536322E+05 -0.84280798E+05 0.63663012E+05 Rj0 = 1.5100 3.0600 4.1400 10.3400 24.8100 70.3000 RKj = 0.60594844E+02 -0.18343542E+02 -0.56504096E+02 0.21738200E+02 -0.41470415E+01 -0.41682080E+01



A.6 – 66


: :


1.0551" 1.0551" 3.5433" 0.4724"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 11.2756" = 0.0000" = 3.5433" = 2 X 1 1

2.3622" 7.7323"

nc = 2 X

pc = pic=

------------------------------


1) Failure mode: Thread stripping 2) Plate size: 460x200x12 mm

= = = =


Remark

ct cc gt tp

U.K. Fasteners: G8.8- -M20 7/8" Oversize holes Material : S275 Fy = -ksi Fu = -ksi

Major parameters



Tested by Test Id.

VI - 34

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

6

18

24

pc cc

li

ct pt

36

42

48

: S275 Experimental Polynominal M. Exponential

30

Material : : :

gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 67


R tf A3 P3


Q3 =


-3





A.6 – 68


: :


0.8583" 0.8583" 3.5433" 0.4724"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 11.2756" = 0.0000" = 3.5433" = 2 X 1 1

2.3622" 7.7323"

nc = 2 X

pc = pic=

------------------------------



= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.

VI - 35

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 69


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.2184E+03 0.5891E+01 0.1262E+03 3 1.00 191.75 5.99 192.57 0.1702E+03 0.6207E+01 0.2160E+03 5 2.01 377.69 12.77 393.43 0.1931E+03 0.7409E+01 0.1749E+03 7 3.01 555.95 21.34 542.08 0.1326E+03 0.9825E+01 0.1241E+03 9 4.01 657.46 30.75 646.39 0.8836E+02 0.7681E+01 0.8714E+02 11 6.02 777.38 40.16 777.91 0.4518E+02 0.2956E+01 0.4998E+02 13 8.02 851.09 44.75 862.04 0.3315E+02 0.1819E+01 0.3610E+02 15 10.03 917.51 47.86 926.62 0.4785E+02 0.1335E+01 0.2862E+02 17 12.03 1001.01 50.24 977.77 0.2167E+02 0.1067E+01 0.2264E+02 19 14.04 1024.19 52.20 1017.73 0.8850E+01 0.8943E+00 0.1724E+02 21 16.05 1041.97 53.87 1047.57 0.4382E+01 0.7737E+00 0.1259E+02 23 18.05 1053.75 55.32 1068.89 0.8850E+01 0.6847E+00 0.8878E+01 25 20.06 1063.63 56.63 1083.74 0.1706E+02 0.6155E+00 0.6044E+01 27 22.06 1102.65 57.80 1093.67 0.5123E+01 0.5606E+00 0.4006E+01 29 24.07 1106.19 58.88 1100.20 0.4515E+00 0.5153E+00 0.2581E+01 31 26.07 1107.96 59.87 1104.34 0.4356E+00 0.4777E+00 0.1626E+01 33 28.08 1107.96 60.80 1106.93 0.0000E+00 0.4456E+00 0.9968E+00 35 30.09 1108.85 61.67 1108.50 -0.8981E+00 0.4180E+00 0.5954E+00 37 32.09 1107.96 62.49 1109.42 0.1399E+01 0.3938E+00 0.3462E+00 39 34.50 1109.73 63.41 1110.03 0.2377E+00 0.3689E+00 0.1715E+00 --------------------------------------------------------------------------------------------------




A.6 – 70


: :


1.0433" 1.0433" 3.5433" 0.4724"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 13.2677" = 0.0000" = 3.5433" = 2 X 1 1

2.3622" 9.7244"

nc = 2 X

pc = pic=

------------------------------



= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.

VI - 36

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

4

12

16

pc cc

li

ct pt

24

28

32


20

Material : : :

gc


8

beam

gt

36

lp

40

nc

ni

nt

A.6 – 71


R tf A3 P3


Q3 =


-3





A.6 – 72


: :


0.8583" 0.8583" 3.5433" 0.5906"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 11.2756" = 0.0000" = 3.5433" = 2 X 1

VI - 37

1

tp

column

------------------------------


2.3622" 7.7323"

nc = 2 X

pc = pic=



= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.


0

250

500

750

1000

1250

1500

1750

2000

2250

2500

0

8

beam

24

32

40

48


16

pc cc

li

ct pt

64


gc

gt

72

lp

80

nc

ni

nt

A.6 – 73


Moment ( kip-inch )

R tf A3 P3


Q3 =


-3





A.6 – 74


: :


1.0433" 1.0433" 3.5433" 0.5906"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 13.2677" = 0.0000" = 3.5433" = 2 X 1 1

2.3622" 9.7244"

nc = 2 X

pc = pic=

------------------------------



= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.

VI - 38

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

7

21

28

pc cc

li

ct pt

42

49

56


35

Material : : :

gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 75


R tf A3 P3


Q3 =


-3





A.6 – 76


: :


0.8268" 0.8268" 3.5433" 0.5906"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 21.9685" = 0.0000" = 3.5433" = 2 X 1 nc = 2 X

1

pc = 2.3622" pic= 18.4252"

------------------------------


1) Failure mode: Bolt fracture 2) Plate size: 720x250x15 mm

= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.

VI - 39

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 77


R tf A3 P3


Q3 =


-3





A.6 – 78


: :


1.0551" 1.0551" 3.5433" 0.4724"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 11.2756" = 4.1890" = 3.5433" = 2 X 2

VI - 40

1

tp

column

------------------------------


2.3622" 3.5433"

nc = 2 X

pc = pic=


1) Failure mode: Column web buckling 2) Plate size: 460x200x12 mm

= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.


0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

7

beam

21

28

35

42

49

56


pc cc

li

ct pt


14

Material : : :

gc

gt

63

lp

70

nc

ni

nt

A.6 – 79


Moment ( kip-inch )

R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.4553E+03 0.5891E+01 0.4800E+03 3 0.50 227.64 2.96 216.74 0.3846E+03 0.5967E+01 0.3862E+03 5 1.01 389.46 6.06 390.21 0.2952E+03 0.6214E+01 0.2965E+03 7 1.51 522.87 9.27 519.97 0.2329E+03 0.6667E+01 0.2257E+03 9 2.02 625.59 12.85 620.67 0.1777E+03 0.7428E+01 0.1723E+03 11 3.03 749.00 21.54 759.67 0.1203E+03 0.9864E+01 0.1112E+03 13 4.04 868.53 30.98 857.33 0.1076E+03 0.7543E+01 0.8606E+02 15 6.06 1022.71 40.28 1012.23 0.6418E+02 0.2919E+01 0.7025E+02 17 8.07 1133.15 44.84 1141.49 0.4797E+02 0.1802E+01 0.5764E+02 19 10.09 1223.45 47.94 1242.30 0.4556E+02 0.1325E+01 0.4204E+02 21 12.11 1313.74 50.33 1312.24 0.3960E+02 0.1059E+01 0.2772E+02 23 14.13 1375.93 52.28 1356.74 0.1771E+02 0.8880E+00 0.1699E+02 25 16.15 1390.93 53.95 1383.38 0.4785E+01 0.7686E+00 0.9930E+01 27 18.17 1397.94 55.41 1398.74 0.2513E+01 0.6801E+00 0.5663E+01 29 20.19 1404.23 56.71 1407.49 0.2022E+01 0.6116E+00 0.3241E+01 31 22.21 1406.30 57.89 1412.57 0.1963E+01 0.5569E+00 0.1923E+01 33 24.22 1411.14 58.96 1415.66 0.1186E+01 0.5123E+00 0.1223E+01 35 26.24 1412.39 59.96 1417.71 0.1743E+01 0.4748E+00 0.8440E+00 37 28.26 1416.53 60.88 1419.18 0.9334E+00 0.4430E+00 0.6276E+00 39 30.28 1417.91 61.75 1420.30 0.6214E+00 0.4156E+00 0.4907E+00 41 32.30 1417.24 62.57 1421.19 -0.5615E+00 0.3915E+00 0.3933E+00 43 34.32 1418.75 63.34 1421.90 0.1681E+01 0.3707E+00 0.3169E+00 45 36.34 1423.88 64.06 1422.48 0.1886E+01 0.3523E+00 0.2541E+00 47 38.35 1425.72 64.76 1422.93 0.1125E+01 0.3356E+00 0.2018E+00 49 40.37 1427.43 65.42 1423.30 0.3048E+00 0.3208E+00 0.1582E+00 51 42.39 1427.95 66.06 1423.58 0.3765E+00 0.3071E+00 0.1224E+00 53 44.41 1428.27 66.67 1423.79 0.5622E-01 0.2947E+00 0.9359E-01 --------------------------------------------------------------------------------------------------




A.6 – 80


: :


1.0433" 1.0433" 3.5433" 0.4724"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 13.2677" = 6.1811" = 3.5433" = 2 X 2

VI - 41

1

tp

column

------------------------------


2.3622" 3.5433"

nc = 2 X

pc = pic=



= = = =


Remark

ct cc gt tp


Major parameters



Tested by Test Id.


0

300

600

900

1200

1500

1800

2100

2400

2700

3000

0

8

beam

24

32

40

48

56

64


pc cc

li

ct pt


16

Material : : :

gc

gt

72

lp

80

nc

ni

nt

A.6 – 81


Moment ( kip-inch )

R tf A3 P3


Q3 =


-3





A.6 – 82


: :


1.0551" 1.0551" 3.5433" 0.5906"

pt = 2.3622" pit= 3.5433" gi = 3.5433" nt = 2 X 1

li pi gc ni

= 11.2756" = 4.1890" = 3.5433" = 2 X 2 1

2.3622" 3.5433"

nc = 2 X

pc = pic=

------------------------------



= = = =


Remark

ct cc gt tp


Major parameters

B.Bose et al. (1996) 10


Tested by Test Id.

VI - 42

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

8

24

32

pc cc

li

ct pt

48

56

64


40

Material : : :

gc


16

beam

gt

72

lp

80

nc

ni

nt

A.6 – 83


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1886E+03 0.8467E+01 0.7934E+02 3 1.00 174.82 8.62 175.07 0.1729E+03 0.8922E+01 0.2204E+03 5 2.00 374.34 18.25 390.36 0.2260E+03 0.1062E+02 0.2005E+03 7 3.00 581.38 30.53 570.28 0.1571E+03 0.1409E+02 0.1602E+03 9 4.00 719.42 44.09 714.62 0.1298E+03 0.1111E+02 0.1307E+03 11 5.99 943.10 57.60 939.74 0.9900E+02 0.4291E+01 0.9946E+02 13 7.99 1111.45 64.24 1116.78 0.7519E+02 0.2629E+01 0.7761E+02 15 9.99 1239.82 68.71 1249.33 0.5655E+02 0.1928E+01 0.5489E+02 17 11.99 1353.46 72.15 1337.53 0.5179E+02 0.1539E+01 0.3393E+02 19 14.99 1401.90 76.21 1403.22 0.2453E+01 0.1196E+01 0.1201E+02 21 18.98 1410.26 80.41 1422.65 0.2234E+01 0.9351E+00 0.4306E+00 23 22.98 1419.52 83.81 1420.60 0.1779E+01 0.7744E+00 -0.5183E+00 25 26.97 1425.54 86.67 1421.77 0.1894E+01 0.6651E+00 0.1162E+01 27 30.97 1434.47 89.16 1429.16 0.2272E+01 0.5852E+00 0.2373E+01 29 34.97 1441.09 91.37 1439.48 0.1509E+01 0.5241E+00 0.2651E+01 31 38.96 1448.92 93.36 1449.56 0.1657E+01 0.4759E+00 0.2340E+01 33 42.96 1455.80 95.19 1457.89 0.2097E+01 0.4365E+00 0.1813E+01 35 46.95 1464.37 96.86 1464.07 0.1144E+01 0.4039E+00 0.1295E+01 37 50.95 1465.49 98.42 1468.37 0.3982E+00 0.3763E+00 0.8722E+00 --------------------------------------------------------------------------------------------------




A.6 – 84


: :


Remark

ct cc gt tp

0.9842" 0.9842" 3.5433" 0.5906"

pt = 1.9685" pit= 10.2362" gi = 3.5433" nt = 2 X 1

= 13.7795" = 0.0000" = 3.5433" = 2 X 1


li pi gc ni

Major parameters

1) Plate size: 500x200x15 mm 2)

= = = =

U.K.

1

1.9685" 3.5433"

nc = 2 X

pc = pic=


N.D.Brown & D.Anderson (2001) TEST1


Tested by Test Id.

VI - 43

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

3

9

pc cc

li

ct pt

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.6 – 85


R tf A3 P3


Q3 =


-3





A.6 – 86


: :


pt = 2.3622" gt = 3.5433" nt = 2 X 1


0.4724" 0.4724" 0.3937"

pc =

2.3622"

------------------------------


li = 5.3543" gc = 3.5433" nc = 2 X 1

Major parameters


Remark

ct = cc = tp =

Ireland

Fasteners: G8.8- -M20 7/8" Oversize holes Material : G43 Fy = -ksi Fu = -ksi

A.W.Thomson & B.M.Broderick (2002) J1-M


Tested by Test Id.

VI - 44

0

55

110

165

220

275

330

385

440

495

550

tp

column

Moment ( kip-inch )


0

10

30

40

60

70

pc cc

li

ct pt

80

: G43 Experimental Polynominal M. Exponential

50

Material : : :

gc


20

beam

gt

90

lp

100

nc

ni

nt

A.6 – 87


R tf A3 P3


Q3 =


-3





A.6 – 88


: :


pt = 2.3622" gt = 3.5433" nt = 2 X 1


0.4724" 0.4724" 0.4724"

pc =

2.3622"

------------------------------


li = 5.3543" gc = 3.5433" nc = 2 X 1

Major parameters


Remark

ct = cc = tp =

Ireland

Fasteners: G8.8- -M20 7/8" Oversize holes Material : G43 Fy = -ksi Fu = -ksi



Tested by Test Id.

VI - 45

0

55

110

165

220

275

330

385

440

495

550

tp

column

Moment ( kip-inch )


0

10

30

40

60

70

pc cc

li

ct pt

80


50

Material : : :

gc


20

beam

gt

90

lp

100

nc

ni

nt

A.6 – 89


R tf A3 P3


Q3 =


-3





A.6 – 90


: :


pt = 2.3622" gt = 3.5433" nt = 2 X 1


0.4724" 0.4724" 0.4724"

pc =

2.3622"

------------------------------


li = 5.3543" gc = 3.5433" nc = 2 X 1

Major parameters


Remark

ct = cc = tp =

Ireland

Fasteners: 10.9- -M20 7/8" Oversize holes Material : G43 Fy = -ksi Fu = -ksi



Tested by Test Id.

VI - 46

0

65

130

195

260

325

390

455

520

585

650

tp

column

Moment ( kip-inch )


0

10

30

40

60

70

pc cc

li

ct pt

80


50

Material : : :

gc


20

beam

gt

90

lp

100

nc

ni

nt

A.6 – 91


R tf A3 P3


Q3 =


-3





A.6 – 92


: :


pt = 2.9528" gt = 5.9055" nt = 2 X 1

li = 6.2992" gc = 5.9055" nc = 2 X 1

pc =

2.9528"

------------------------------


1) Failure mode: Fracture of bolt at tension side 2) Plate size: 360x300x15 mm

0.9842" 0.9842" 0.5807"

Major parameters


Remark

ct = cc = tp =

Portugal


A.M.G.Coelho & F.S.K.Bijlaard (2007) F1EP_15_2


Tested by Test Id.

VI - 47

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 93


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1335E+03 0.2866E+02 0.1231E+03 3 2.00 260.62 61.75 261.13 0.1251E+03 0.3595E+02 0.1268E+03 5 4.00 502.53 149.20 506.53 0.1205E+03 0.3760E+02 0.1200E+03 7 6.00 746.61 195.10 741.42 0.1161E+03 0.1448E+02 0.1139E+03 9 8.00 965.78 217.52 957.60 0.9735E+02 0.8882E+01 0.1013E+03 11 10.00 1137.19 232.64 1144.36 0.8331E+02 0.6519E+01 0.8532E+02 13 12.00 1299.19 244.26 1299.52 0.7257E+02 0.5205E+01 0.7022E+02 15 14.00 1427.31 253.77 1427.22 0.6002E+02 0.4364E+01 0.5801E+02 17 16.00 1535.69 261.88 1533.59 0.5137E+02 0.3776E+01 0.4882E+02 19 18.00 1626.46 268.98 1624.08 0.4035E+02 0.3340E+01 0.4200E+02 21 20.00 1704.25 275.31 1702.60 0.3668E+02 0.3003E+01 0.3672E+02 23 22.00 1776.11 281.04 1771.58 0.3231E+02 0.2734E+01 0.3237E+02 25 24.00 1833.48 286.28 1832.43 0.2831E+02 0.2514E+01 0.2854E+02 27 26.00 1882.55 291.12 1885.95 0.2114E+02 0.2330E+01 0.2502E+02 29 28.00 1924.69 295.61 1932.68 0.2066E+02 0.2174E+01 0.2175E+02 31 30.00 1965.31 299.82 1973.08 0.2035E+02 0.2039E+01 0.1870E+02 33 32.00 2006.73 303.84 2007.63 0.2102E+02 0.1921E+01 0.1590E+02 35 34.00 2044.25 307.55 2036.85 0.2552E+01 0.1819E+01 0.1337E+02 37 36.00 1967.04 311.07 1979.18 -0.9165E+02 0.1728E+01 -0.2993E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.55833333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 2 AI = -0.41201032E+03 0.85536224E+04 -0.51033994E+05 0.12760157E+06 -0.14576213E+06 Rj0 = 34.0000 36.9000 RKj = -0.41053624E+02 -0.99174263E+03



A.6 – 94


: :


pt = 2.9528" gt = 5.9055" nt = 2 X 1

li = 6.2992" gc = 5.9055" nc = 2 X 1

pc =

2.9528"

------------------------------


1) Failure mode: Fracture of bolt at tension side 2) Plate size: 310x300x15 mm

0.0000" 0.0000" 0.5764"

Major parameters


Remark

ct = cc = tp =

Portugal




Tested by Test Id.

VI - 48

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 95


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1144E+03 0.2857E+02 0.6990E+02 3 2.00 228.89 61.57 232.72 0.1136E+03 0.3584E+02 0.1188E+03 5 4.00 448.69 148.75 451.21 0.1078E+03 0.3749E+02 0.1041E+03 7 6.00 665.53 194.52 659.30 0.1067E+03 0.1443E+02 0.1042E+03 9 8.00 864.45 216.87 863.49 0.9169E+02 0.8856E+01 0.9838E+02 11 10.00 1038.58 231.95 1047.48 0.8433E+02 0.6499E+01 0.8476E+02 13 12.00 1204.80 243.53 1201.11 0.7166E+02 0.5190E+01 0.6896E+02 15 14.00 1321.84 253.01 1324.73 0.5563E+02 0.4351E+01 0.5519E+02 17 16.00 1427.61 261.10 1424.26 0.4467E+02 0.3765E+01 0.4493E+02 19 18.00 1505.49 268.17 1506.60 0.3959E+02 0.3330E+01 0.3788E+02 21 20.00 1586.28 274.48 1577.32 0.3808E+02 0.2994E+01 0.3313E+02 23 22.00 1650.04 280.20 1640.03 0.2615E+02 0.2726E+01 0.2975E+02 25 24.00 1684.07 285.42 1696.75 0.1822E+02 0.2506E+01 0.2704E+02 27 26.00 1737.21 290.25 1748.35 0.2676E+02 0.2323E+01 0.2459E+02 29 28.00 1791.07 294.73 1795.14 0.2501E+02 0.2167E+01 0.2220E+02 31 30.00 1836.28 298.93 1837.17 0.2212E+02 0.2033E+01 0.1982E+02 33 32.00 1880.53 302.93 1874.45 0.2212E+02 0.1915E+01 0.1747E+02 35 34.00 1895.85 306.63 1899.39 -0.2732E+02 0.1813E+01 0.7497E+01 37 36.00 1782.61 310.14 1783.77 -0.6244E+02 0.1723E+01 -0.5887E+02 39 38.00 1672.57 313.54 1672.43 -0.5183E+02 0.1641E+01 -0.5244E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.57500000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.10501358E+04 0.16394160E+05 -0.84887052E+05 0.19297897E+06 -0.20362324E+06 Rj0 = 33.0000 34.0000 37.0000 RKj = -0.76868807E+01 -0.64215242E+02 0.84200095E+01



A.6 – 96


: :


pt = 2.9528" gt = 5.9055" nt = 2 X 1

li = 6.2992" gc = 5.9055" nc = 2 X 1

pc =

2.9528"

------------------------------


1) Failure mode: weld failure along inner welds zone 2) Plate size: 360x300x10 mm

0.9842" 0.9842" 0.3996"

Major parameters


Remark

ct = cc = tp =

Portugal




Tested by Test Id.

VI - 49

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

7

21

pc cc

li

ct pt

28

35

42

49

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 97


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.9628E+02 0.2468E+02 0.9849E+02 3 2.00 192.57 53.17 192.55 0.9355E+02 0.3096E+02 0.9073E+02 5 4.00 361.72 128.48 360.09 0.7354E+02 0.3238E+02 0.7696E+02 7 6.00 499.42 168.01 501.19 0.6614E+02 0.1247E+02 0.6432E+02 9 8.00 616.24 187.31 618.07 0.5322E+02 0.7649E+01 0.5278E+02 11 10.00 712.45 200.34 713.37 0.4325E+02 0.5614E+01 0.4284E+02 13 12.00 792.28 210.34 790.79 0.3515E+02 0.4483E+01 0.3493E+02 15 14.00 857.78 218.53 854.46 0.2834E+02 0.3758E+01 0.2904E+02 17 16.00 907.59 225.51 908.08 0.2429E+02 0.3252E+01 0.2482E+02 19 18.00 952.23 231.63 954.54 0.2095E+02 0.2877E+01 0.2180E+02 21 20.00 993.88 237.08 995.79 0.1958E+02 0.2586E+01 0.1954E+02 23 22.00 1030.81 242.01 1033.00 0.1846E+02 0.2355E+01 0.1772E+02 25 24.00 1067.33 246.52 1066.82 0.1704E+02 0.2165E+01 0.1612E+02 27 26.00 1099.40 250.69 1097.55 0.1561E+02 0.2006E+01 0.1462E+02 29 28.00 1127.78 254.56 1125.34 0.1320E+02 0.1872E+01 0.1317E+02 31 30.00 1154.17 258.19 1150.26 0.1091E+02 0.1756E+01 0.1176E+02 33 32.00 1170.78 261.65 1172.40 0.7991E+01 0.1654E+01 0.1039E+02 35 34.00 1191.02 264.84 1191.87 0.1252E+02 0.1566E+01 0.9090E+01 37 36.00 1217.91 267.87 1220.93 0.1691E+02 0.1488E+01 0.1393E+02 39 38.00 1252.05 270.81 1247.65 0.9506E+01 0.1417E+01 0.1281E+02 41 40.00 1182.25 273.55 1159.14 -0.6065E+02 0.1355E+01 -0.1013E+03 43 42.00 1105.28 276.23 1119.88 -0.2546E+02 0.1297E+01 -0.2007E+02 45 44.00 1071.73 278.80 1078.93 -0.1242E+02 0.1245E+01 -0.2086E+02 47 46.00 1053.10 281.20 1036.52 -0.6495E+01 0.1198E+01 -0.2154E+02 --------------------------------------------------------------------------------------------------




A.6 – 98


: :


pt = 2.9528" gt = 5.9055" nt = 2 X 1

li = 6.2992" gc = 5.9055" nc = 2 X 1

pc =

2.9528"

------------------------------


1) Failure mode: weld failure along inner welds zone 2) Plate size: 310x300x10 mm

0.0000" 0.0000" 0.4035"

Major parameters


Remark

ct = cc = tp =

Portugal




Tested by Test Id.

VI - 50

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

7

21

pc cc

li

ct pt

28

35

42

49

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 99


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.7042E+02 0.2477E+02 0.6628E+02 3 2.00 130.34 53.38 131.90 0.5746E+02 0.3108E+02 0.5421E+02 5 4.00 231.46 128.98 229.85 0.4711E+02 0.3251E+02 0.4876E+02 7 6.00 332.64 168.67 335.64 0.5354E+02 0.1251E+02 0.5678E+02 9 8.00 455.00 188.05 451.76 0.6331E+02 0.7679E+01 0.5769E+02 11 10.00 565.49 201.12 560.84 0.4842E+02 0.5636E+01 0.5044E+02 13 12.00 650.08 211.16 651.47 0.3819E+02 0.4500E+01 0.4008E+02 15 14.00 717.15 219.39 721.74 0.3095E+02 0.3773E+01 0.3053E+02 17 16.00 775.52 226.40 775.22 0.2480E+02 0.3265E+01 0.2340E+02 19 18.00 817.37 232.53 817.01 0.1862E+02 0.2888E+01 0.1876E+02 21 20.00 853.09 238.01 851.53 0.1599E+02 0.2596E+01 0.1602E+02 23 22.00 881.22 242.96 881.87 0.1452E+02 0.2364E+01 0.1446E+02 25 24.00 911.79 247.49 909.76 0.1542E+02 0.2173E+01 0.1349E+02 27 26.00 937.84 251.67 935.96 0.1075E+02 0.2014E+01 0.1273E+02 29 28.00 958.61 255.56 960.67 0.9980E+01 0.1879E+01 0.1197E+02 31 30.00 979.22 259.20 983.77 0.1182E+02 0.1763E+01 0.1111E+02 33 32.00 1005.16 262.67 1005.06 0.1297E+02 0.1660E+01 0.1016E+02 35 34.00 1027.35 265.88 1024.36 0.8636E+01 0.1572E+01 0.9134E+01 37 36.00 1018.66 268.92 1018.65 -0.1674E+02 0.1494E+01 -0.1484E+02 39 38.00 985.17 271.87 987.93 -0.1591E+02 0.1423E+01 -0.1588E+02 41 40.00 958.87 274.62 955.18 -0.1159E+02 0.1360E+01 -0.1686E+02 --------------------------------------------------------------------------------------------------




A.6 – 100


: :


pt = 1.9134" gt = 4.9331" nt = 2 X 1


0.0000" 0.0000" 0.4724"


Remark

ct = cc = tp =

Netherlands

1.9134"

------------------------------


li = 7.5906" gc = 4.9331" nc = 2 X 1

pc =

Fasteners: G8.8- -M24 33/32" Oversize holes Material : -Fy = 42.70 ksi Fu = -ksi

Major parameters

P. Zoetemeijer (1981) 16

Column : -Beam : HE300A Plate thickness : 12 mm

Tested by Test Id.

VI - 51

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

9

27

pc cc

li

ct pt

36

45

54

63

72


gc


18

beam

gt

81

lp

90

nc

ni

nt

A.6 – 101


R tf A3 P3


Q3 =


-3





A.6 – 102


: :


pt = 1.9134" gt = 4.9331" nt = 2 X 1


0.0000" 0.0000" 0.6299"


Remark

ct = cc = tp =

Netherlands

1.9134"

------------------------------


li = 7.5906" gc = 4.9331" nc = 2 X 1

pc =


Major parameters



Tested by Test Id.

VI - 52

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

7

21

pc cc

li

ct pt

28

35

42

49

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 103


R tf A3 P3


Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.46558333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.66084328E+03 0.97364735E+04 -0.48369591E+05 0.11559345E+06 -0.12694025E+06 Rj0 = 15.9500 27.9100 39.8700 RKj = 0.33631869E+01 0.81289487E+01 0.52191432E+01



A.6 – 104


: :


pt = 2.7402" gt = 4.9331" nt = 2 X 1

1) Failure mode: weld failure 2) Plate size: 290x300x12 mm

0.0000" 0.0000" 0.4724"


Remark

ct = cc = tp =

Netherlands

2.7402"

------------------------------


li = 5.9370" gc = 4.9331" nc = 2 X 1

pc =


Major parameters



Tested by Test Id.

VI - 53

0

100

200

300

400

500

600

700

800

900

1000

tp

column

Moment ( kip-inch )


0

9

27

pc cc

li

ct pt

36

45

54

63

72


gc


18

beam

gt

81

lp

90

nc

ni

nt

A.6 – 105


R tf A3 P3


Q3 =


-3





A.6 – 106


: :


pt = 2.7402" gt = 4.9331" nt = 2 X 1


0.0000" 0.0000" 0.6299"


Remark

ct = cc = tp =

Netherlands

2.7402"

------------------------------


li = 5.9370" gc = 4.9331" nc = 2 X 1

pc =


Major parameters



Tested by Test Id.

VI - 54

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

9

27

pc cc

li

ct pt

36

45

54

63

72


gc


18

beam

gt

81

lp

90

nc

ni

nt

A.6 – 107


R tf A3 P3


Q3 =


-3


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.59100000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.11778337E+03 0.23850598E+04 -0.22190129E+05 0.62247707E+05 -0.70441921E+05 Rj0 = 23.9700 33.9500 51.9300 RKj = 0.11001452E+01 0.21958472E+01 0.19766719E+01



A.6 – 108


: :


pt = 2.0118" gt = 3.8661" nt = 2 X 1


0.0000" 0.0000" 0.4724"


Remark

ct = cc = tp =

Netherlands

2.0118"


li = 11.7244" gc = 3.8661" nc = 2 X 1

pc =


Major parameters



Tested by Test Id.

VI - 55

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

7

21

pc cc

li

ct pt

28

35

42

49

56


gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 109


R tf A3 P3


Q3 =


-3





A.6 – 110


: :


pt = 2.0118" gt = 3.8661" nt = 2 X 1

1) Failure mode: bolt failure 2) Plate size: 400x180x16 mm

0.0000" 0.0000" 0.6299"


Remark

ct = cc = tp =

Netherlands

2.0118"

------------------------------


li = 11.7244" gc = 3.8661" nc = 2 X 1

pc =


Major parameters



Tested by Test Id.

VI - 56

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

6

18

pc cc

li

ct pt

24

30

36

42

48


gc


12

beam

gt

54

lp

60

nc

ni

nt

A.6 – 111


R tf A3 P3


Q3 =


-3





A.6 – 112


: :


pt = 2.1378" gt = 4.1181" nt = 2 X 1

1) Failure mode: bolt failure 2) Plate size: 400x180x32 mm

0.0000" 0.0000" 1.2598"


Remark

ct = cc = tp =

Netherlands

2.1378"

------------------------------


li = 11.4724" gc = 4.1181" nc = 2 X 1

pc =


Major parameters



Tested by Test Id.

VI - 57

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

3

9

pc cc

li

ct pt

12

15

18

21

24


gc


6

beam

gt

27

lp

30

nc

ni

nt

A.6 – 113


R tf A3 P3


Q3 =


-3

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.8676E+03 0.1644E+02 0.9413E+03 3 0.19 173.51 3.13 187.25 0.9990E+03 0.1648E+02 0.9595E+03 5 0.39 389.55 6.42 358.34 0.9448E+03 0.1657E+02 0.7381E+03 7 1.00 622.69 16.73 630.97 0.2980E+03 0.1733E+02 0.2572E+03 9 2.00 845.50 35.45 837.69 0.2002E+03 0.2063E+02 0.2009E+03 11 3.00 1027.61 59.30 1028.98 0.1627E+03 0.2737E+02 0.1743E+03 13 4.00 1169.86 85.63 1173.23 0.1290E+03 0.2157E+02 0.1184E+03 15 5.00 1292.52 101.93 1286.89 0.1156E+03 0.1229E+02 0.1111E+03 17 5.99 1399.30 111.88 1395.16 0.9938E+02 0.8333E+01 0.1066E+03 19 6.99 1491.39 119.10 1496.02 0.9311E+02 0.6310E+01 0.9350E+02 21 7.99 1583.25 124.76 1579.64 0.7431E+02 0.5108E+01 0.7292E+02 23 8.99 1642.15 129.45 1641.12 0.5027E+02 0.4312E+01 0.5008E+02 25 9.99 1670.19 133.46 1680.48 0.1178E+02 0.3746E+01 0.2919E+02 27 10.99 1667.27 136.99 1662.78 -0.3295E+02 0.3321E+01 -0.6386E+02 29 11.99 1616.32 140.14 1592.23 -0.8159E+02 0.2990E+01 -0.7657E+02 31 12.99 1503.40 142.99 1510.88 -0.1084E+03 0.2725E+01 -0.8557E+02 33 13.99 1421.73 145.60 1422.06 -0.5817E+02 0.2506E+01 -0.9167E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.14575000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = -0.15519684E+04 0.23096530E+05 -0.11533863E+06 0.27113900E+06 -0.29501651E+06 Rj0 = 3.5000 10.4900 13.9900 RKj = -0.26258625E+02 -0.76071907E+02 0.35959488E+02



A.6 – 114


: :

G. Shi et al (2007) JD1


Remark

ct cc gt tp

0.3937" 0.3937" 4.2520" 0.7874"

pt = 2.4409" pit= 3.4646" gi = 4.2520" nt = 2 X 1

li pi gc ni

= 6.9291" = 0.0000" = 4.2520" = 2 X 1 1

2.4409" 3.4646"

nc = 2 X

pc = pic=


1) Plate size: 320x200x20 mm 2) Column flange thickness is taken the same as the end-plate thickness

= = = =

China Fasteners: 10.9- -M20 7/8" Oversize holes Material : Q345 Fy = 54.04 ksi Fu = 77.89 ksi

Major parameters

Column : H300x250x8x12 Beam : H300x200x8x12 Plate thickness : 20 mm Stiffener thickness : 0.3937"

Tested by Test Id.

VI - 58

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

7

21

pc cc

li

ct pt

28

35

42

49

56

Material : Q345 Fy = 54.04 ksi : Experimental : Polynominal : M. Exponential

gc


14

beam

gt

63

lp

70

nc

ni

nt

A.6 – 115


( R : X 1/1000 radians )

A3 = P3 =

2.040000 5

K = Q1 =

0.035782 0 Q2 =


Q3 =


-1





A.6 – 116


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 15.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 1.3750" tbw= 0.3350" n = 2 X 5


Major parameters

W.H.Sommer (1969) TEST 5

Column : -Beam : W18X45 Plate thickness : 1/4"

Tested by Test Id.

VII -

1

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )

Connection type : Header plate connections Mode : All bolted

0

tbw

15

45

60

75

90

lc

p cc

ct p

lt

lp

n

105 120 135 150

g


30


beam

A.7 – 1


( R : X 1/1000 radians ) R = Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) t = 0.250000" w = 0.335000" A3 = 2.400000 K = 0.287779 P3 = 5 Q1 = -2 Q2 = -7

Q3 =



0.59310846E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.9300E+02 0.6813E+02 0.1051E+03 0.7477E+02 3 0.40 42.80 27.25 43.24 29.87 0.1008E+03 0.6798E+02 0.1097E+03 0.7446E+02 5 1.10 115.00 74.46 118.52 81.42 0.1602E+03 0.6669E+02 0.1030E+03 0.7258E+02 7 2.05 211.50 135.68 206.36 148.28 0.7462E+02 0.6137E+02 0.8076E+02 0.6782E+02 9 3.60 296.00 218.69 301.77 245.20 0.4000E+02 0.4502E+02 0.4407E+02 0.5681E+02 11 8.65 387.50 356.85 392.84 442.35 0.1337E+02 0.1703E+02 0.8638E+01 0.2444E+02 13 17.00 479.50 452.52 481.58 551.83 0.8690E+01 0.8125E+01 0.1047E+02 0.6413E+01 15 25.20 543.33 506.82 546.30 584.46 0.6833E+01 0.5484E+01 0.6195E+01 0.2384E+01 17 33.20 598.00 545.14 596.88 597.71 0.7347E+01 0.4219E+01 0.6884E+01 0.1131E+01 19 40.53 655.33 573.29 651.34 604.01 0.7819E+01 0.3508E+01 0.7772E+01 0.6483E+00 21 47.57 703.33 596.20 705.23 607.66 0.5742E+01 0.3033E+01 0.7360E+01 0.4120E+00 23 54.30 742.00 615.43 751.12 609.96 0.6669E+01 0.2694E+01 0.6198E+01 0.2821E+00 25 60.10 791.00 630.48 783.72 611.38 0.9430E+01 0.2460E+01 0.5046E+01 0.2107E+00 27 63.30 829.00 638.11 827.01 612.00 0.1578E+02 0.2351E+01 0.2098E+02 0.1814E+00 29 66.10 877.00 644.63 885.08 612.48 0.1863E+02 0.2262E+01 0.2050E+02 0.1601E+00 31 71.00 984.00 655.33 983.72 613.19 0.2105E+02 0.2125E+01 0.1978E+02 0.1301E+00 33 74.80 1060.00 663.16 1058.00 613.65 0.1842E+02 0.2031E+01 0.1933E+02 0.1119E+00 35 79.00 1130.00 671.59 1138.30 614.08 0.1484E+02 0.1936E+01 0.1893E+02 0.9545E-01 37 86.90 1220.00 686.32 1209.25 614.74 0.9588E+01 0.1782E+01 0.8742E+01 0.7233E-01 39 93.00 1270.00 696.81 1261.76 615.14 0.6557E+01 0.1682E+01 0.8493E+01 0.5935E-01 41 99.10 1300.00 706.72 1313.04 615.47 0.4918E+01 0.1593E+01 0.8333E+01 0.4930E-01 ----------------------------------------------------------------------------------------------------------------------------



Frye and Morris polynominal model : g = 4.000000" d = 15.000000" A1 = 5.100000 A2 = 6.200000 P1 = 1 P2 = 3


A.7 – 2


: :


1) 2)

1.5000" 4.0000"

p = lp =

3.0000" 9.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 13.3750" tbw= 0.4410" n = 2 X 3


Major parameters



Tested by Test Id.

VII -

2

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

9

27

36

45

54


18

tbw

g

lc

p cc

ct p

lt

lp

72

81


beam

90

n

A.7 – 3



Q3 =



0.14105882E+06

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1048E+02 0.2414E+02 0.2656E+02 0.2455E+02 3 4.50 40.70 90.39 42.07 68.24 0.7251E+01 0.1285E+02 0.7150E+01 0.9879E+01 5 8.35 69.65 124.66 68.59 98.05 0.7810E+01 0.6279E+01 0.7528E+01 0.6092E+01 7 12.47 103.40 145.08 103.39 118.58 0.8515E+01 0.3998E+01 0.8978E+01 0.4091E+01 9 17.00 142.00 160.36 142.34 134.10 0.7992E+01 0.2879E+01 0.7902E+01 0.2873E+01 11 21.27 174.00 171.30 172.93 144.76 0.7500E+01 0.2296E+01 0.6572E+01 0.2174E+01 13 23.70 211.00 176.59 209.42 149.69 0.6550E+02 0.2063E+01 0.7593E+02 0.1887E+01 15 24.80 283.00 178.84 292.95 151.70 0.1417E+03 0.1973E+01 0.7596E+02 0.1776E+01 17 25.20 364.00 179.62 361.67 152.41 0.2450E+03 0.1942E+01 0.2676E+03 0.1739E+01 19 25.55 456.50 180.30 455.34 153.01 0.2833E+03 0.1917E+01 0.2676E+03 0.1707E+01 21 25.85 538.00 180.87 535.63 153.52 0.2600E+03 0.1895E+01 0.2677E+03 0.1680E+01 23 26.20 625.00 181.53 629.33 154.10 0.2400E+03 0.1871E+01 0.2677E+03 0.1649E+01 25 26.90 720.50 182.84 719.38 155.23 0.9500E+02 0.1823E+01 0.7304E+02 0.1591E+01 27 28.20 817.00 185.13 814.49 157.24 0.6125E+02 0.1744E+01 0.7330E+02 0.1491E+01 29 30.15 904.50 188.41 906.16 160.01 0.3347E+02 0.1637E+01 0.2879E+02 0.1358E+01 31 33.10 991.50 193.03 992.21 163.76 0.2695E+02 0.1499E+01 0.2953E+02 0.1189E+01 33 36.80 1085.00 198.30 1080.81 167.84 0.2368E+02 0.1359E+01 0.1858E+02 0.1020E+01 35 40.65 1150.00 203.30 1152.58 171.48 0.1026E+02 0.1240E+01 0.1857E+02 0.8801E+00 37 44.35 1215.00 207.74 1220.13 174.53 0.2571E+02 0.1144E+01 0.1783E+02 0.7718E+00 39 48.13 1290.00 211.92 1285.04 177.27 0.1475E+02 0.1063E+01 0.1638E+02 0.6809E+00 41 52.20 1350.00 216.08 1347.49 179.87 0.1115E+02 0.9881E+00 0.1424E+02 0.6004E+00 43 56.10 1380.00 219.81 1398.40 182.09 -0.4917E+02 0.9267E+00 0.1182E+02 0.5362E+00 45 57.02 1294.00 220.66 1282.29 182.57 -0.1438E+03 0.9134E+00 -0.1265E+03 0.5226E+00 47 57.66 1202.00 221.24 1201.19 182.91 -0.1438E+03 0.9044E+00 -0.1269E+03 0.5135E+00 49 58.30 1110.00 221.82 1119.82 183.23 -0.1438E+03 0.8955E+00 -0.1274E+03 0.5046E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.11108333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = -0.50562273E+03 0.12738751E+05 -0.91006044E+05 0.26142970E+06 -0.32168317E+06 Rj0 = 0.0000 23.4000 25.0000 26.4000 29.0000 34.9000 56.1000 RKj = -0.20126044E+02 0.69600663E+02 0.19161748E+03 -0.19480933E+03 -0.44989307E+02 -0.11569984E+02 -0.13772868E+03



A.7 – 4



: :

1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 12.0000"

1.5000" 0.2500"

VII -


3

tp

column

2000

------------------------------

0

200

400

600

800

1000

1200

1400

1600

1800


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 10.3750" tbw= 0.4400" n = 2 X 4


Major parameters



Tested by Test Id.


Moment ( kip-inch )

0

9

27

lc

p cc

ct p

lt

lp

36

45

54

63

72

81


tbw

g


18

beam

90

n

A.7 – 5



Q3 =



0.12939963E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.6576E+02 0.4674E+02 0.6956E+02 0.5654E+02 3 1.60 55.40 73.62 56.34 79.95 0.2425E+02 0.4425E+02 0.2578E+02 0.4294E+02 5 3.45 113.75 145.27 113.46 146.58 0.4500E+02 0.3201E+02 0.3446E+02 0.2994E+02 7 5.40 177.00 195.19 176.69 195.57 0.2615E+02 0.2030E+02 0.2829E+02 0.2098E+02 9 8.90 235.25 247.66 242.44 251.51 0.1102E+02 0.1130E+02 0.1119E+02 0.1208E+02 11 13.30 283.75 287.06 279.93 291.73 0.1102E+02 0.7216E+01 0.8398E+01 0.6874E+01 13 17.30 322.50 312.08 319.52 314.03 0.8053E+01 0.5474E+01 0.1128E+02 0.4511E+01 15 20.50 361.00 328.13 367.78 326.52 0.2114E+02 0.4610E+01 0.1951E+02 0.3373E+01 17 23.10 424.00 339.42 417.92 334.41 0.1029E+03 0.4096E+01 0.1891E+02 0.2727E+01 19 23.70 506.50 341.86 517.79 336.01 0.1675E+03 0.3993E+01 0.1663E+03 0.2603E+01 21 24.10 574.00 343.45 584.28 337.03 0.1700E+03 0.3928E+01 0.1661E+03 0.2525E+01 23 24.55 656.50 345.21 658.99 338.15 0.1940E+03 0.3858E+01 0.1659E+03 0.2441E+01 25 25.05 753.50 347.13 741.88 339.35 0.1940E+03 0.3783E+01 0.1657E+03 0.2352E+01 27 25.57 850.66 349.08 827.40 340.54 0.1825E+03 0.3708E+01 0.1654E+03 0.2265E+01 29 26.10 948.00 351.04 915.51 341.73 0.1510E+03 0.3635E+01 0.1651E+03 0.2180E+01 31 27.10 1040.00 354.64 1080.27 343.83 0.7716E+02 0.3505E+01 0.1645E+03 0.2033E+01 33 29.57 1140.00 362.94 1150.20 348.45 0.4054E+02 0.3225E+01 0.2759E+02 0.1725E+01 35 32.50 1240.00 371.91 1235.65 353.08 0.2941E+02 0.2953E+01 0.3004E+02 0.1439E+01 37 35.90 1335.00 381.49 1334.81 357.52 0.2647E+02 0.2691E+01 0.2835E+02 0.1186E+01 39 39.25 1430.00 390.22 1427.51 361.16 0.3030E+02 0.2476E+01 0.2705E+02 0.9946E+00 41 43.20 1530.00 399.50 1532.05 364.73 0.2174E+02 0.2270E+01 0.2595E+02 0.8213E+00 43 47.80 1595.00 409.47 1595.42 368.14 0.6522E+01 0.2071E+01 0.1669E+01 0.6694E+00 45 51.90 1605.00 417.71 1601.27 370.66 -0.2780E+01 0.1923E+01 0.1218E+01 0.5660E+00 47 54.23 1545.00 422.04 1547.78 371.92 -0.1048E+03 0.1850E+01 -0.1058E+03 0.5173E+00 49 55.27 1435.00 423.97 1436.64 372.45 -0.1048E+03 0.1818E+01 -0.1059E+03 0.4972E+00 51 56.33 1325.00 425.88 1325.44 372.97 -0.1048E+03 0.1788E+01 -0.1059E+03 0.4783E+00 53 57.38 1215.00 427.75 1214.18 373.46 -0.1048E+03 0.1759E+01 -0.1060E+03 0.4604E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.58250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.55769000E+03 -0.50981917E+04 0.11876062E+05 -0.18623086E+04 -0.17886657E+05 Rj0 = 19.1000 23.1000 27.1000 30.8000 45.5000 53.7000 RKj = 0.74952921E+01 0.14766549E+03 -0.13535064E+03 0.41795480E+01 -0.23456179E+02 -0.10685890E+03



A.7 – 6


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 15.0000"

1.5000" 0.2500"

VII -


4

tp

column

Moment ( kip-inch )

------------------------------

0

200

400

600

-----------------------------No Moment Rotation (k-in) (radians) X 1/1000 -----------------------------51 1440.00 41.50 52 1440.00 43.50 53 1397.78 43.69 54 1355.55 43.88 2000 55 1313.33 44.07 56 1271.11 44.26 1800 57 1228.89 44.44 58 1186.66 44.63 1600 59 1144.44 44.82 60 1102.22 45.01 1400 61 1060.00 45.20 1200 62 1020.00 47.40 63 982.75 47.95 1000 64 945.50 48.50 65 908.25 49.05 800 66 871.00 49.60

for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 7.3750" tbw= 0.4410" n = 2 X 5


Major parameters



Tested by Test Id.


0

8

24

lc

p cc

ct p

lt

lp

32

40

48

56

64

72


tbw

g


16

beam

80

n

A.7 – 7


R t A3 P3

= Sum ( Ai X ( K*Bm )**Pi X 10**Qi ) = 0.250000" w = 0.441000" = 2.400000 K = 0.250820 = 5 Q1 = -2 Q2 =

( R : X 1/1000 radians )

-7

Q3 =



0.14160242E+06

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.8800E+02 0.7817E+02 0.8430E+02 0.1092E+03 3 0.50 44.70 39.07 45.86 52.68 0.9477E+02 0.7789E+02 0.9465E+02 0.1007E+03 5 1.10 106.00 85.43 100.62 109.46 0.9015E+02 0.7651E+02 0.8602E+02 0.8853E+02 7 2.10 172.00 159.18 175.69 188.51 0.6337E+02 0.6993E+02 0.6479E+02 0.7018E+02 9 2.90 221.00 211.57 222.46 239.73 0.6000E+02 0.6063E+02 0.5303E+02 0.5829E+02 11 3.70 268.00 255.96 261.65 282.38 0.5043E+02 0.5043E+02 0.4541E+02 0.4868E+02 13 5.00 316.00 312.29 314.73 337.58 0.3316E+02 0.3706E+02 0.3662E+02 0.3693E+02 15 6.70 364.00 365.33 368.47 390.91 0.2824E+02 0.2637E+02 0.2690E+02 0.2657E+02 17 8.40 412.00 404.47 408.02 429.93 0.2527E+02 0.2021E+02 0.2041E+02 0.1978E+02 19 12.30 484.00 467.53 488.45 488.00 0.1588E+02 0.1314E+02 0.2490E+02 0.1114E+02 21 16.50 539.00 514.48 541.25 524.51 0.1100E+02 0.9614E+01 0.2067E+02 0.6760E+01 23 20.85 580.50 551.50 581.50 548.29 0.9998E+01 0.7581E+01 0.1113E+02 0.4408E+01 25 24.55 614.50 577.34 615.89 562.26 0.7778E+01 0.6455E+01 0.6315E+01 0.3228E+01 27 27.10 654.00 593.02 628.87 569.73 0.5198E+02 0.5867E+01 0.3878E+01 0.2662E+01 29 27.90 703.00 597.69 724.22 571.80 0.1031E+03 0.5705E+01 0.1181E+03 0.2513E+01 31 28.45 775.50 600.81 788.79 573.16 0.1318E+03 0.5599E+01 0.1167E+03 0.2418E+01 33 29.00 848.00 603.87 852.56 574.46 0.1339E+03 0.5497E+01 0.1152E+03 0.2328E+01 35 29.47 911.33 606.43 906.05 575.53 0.1357E+03 0.5414E+01 0.1140E+03 0.2255E+01 37 30.10 976.50 609.84 977.71 576.93 0.8376E+02 0.5306E+01 0.1123E+03 0.2161E+01 39 30.70 1043.34 613.01 1044.64 578.20 0.1667E+03 0.5207E+01 0.1108E+03 0.2077E+01 41 31.10 1110.00 615.09 1088.76 579.02 0.1444E+03 0.5144E+01 0.1098E+03 0.2024E+01 43 31.90 1190.00 619.18 1175.79 580.60 0.1000E+03 0.5022E+01 0.1078E+03 0.1923E+01 45 32.77 1270.00 623.50 1268.34 582.22 0.8572E+02 0.4896E+01 0.1058E+03 0.1822E+01 47 33.70 1350.00 627.88 1366.08 583.87 0.6961E+02 0.4773E+01 0.1037E+03 0.1721E+01 49 36.80 1400.00 642.21 1405.07 588.75 0.1310E+02 0.4395E+01 0.9714E+01 0.1438E+01 51 41.50 1440.00 661.62 1434.60 594.72 0.3913E+01 0.3939E+01 0.3359E+01 0.1122E+01 53 43.69 1397.78 670.04 1397.34 597.05 -0.2235E+03 0.3758E+01 -0.2226E+03 0.1008E+01 55 44.07 1313.33 671.46 1313.17 597.43 -0.2235E+03 0.3729E+01 -0.2229E+03 0.9901E+00 57 44.44 1228.89 672.86 1228.91 597.80 -0.2236E+03 0.3700E+01 -0.2232E+03 0.9726E+00 59 44.82 1144.44 674.26 1144.52 598.16 -0.2235E+03 0.3672E+01 -0.2235E+03 0.9555E+00 61 45.20 1060.00 675.64 1060.03 598.52 -0.2073E+03 0.3644E+01 -0.2238E+03 0.9389E+00 63 47.95 982.75 685.40 982.82 600.95 -0.6773E+02 0.3455E+01 -0.6749E+02 0.8293E+00 65 49.05 908.25 689.18 908.31 601.84 -0.6773E+02 0.3385E+01 -0.6797E+02 0.7906E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.48833333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = -0.57861081E+03 0.13810048E+05 -0.98653630E+05 0.27971429E+06 -0.33444256E+06 Rj0 = 12.3000 16.5000 25.9000 27.1000 33.7000 43.5000 45.2000 47.4000 RKj = -0.20913863E+02 -0.15824918E+02 0.36797387E+01 0.11635427E+03 -0.87999841E+02 -0.22398412E+03 0.20618600E+03 -0.48344144E+02



A.7 – 8


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 18.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 4.3750" tbw= 0.4410" n = 2 X 6


Major parameters



Tested by Test Id.

VII -

5

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

8

24

32

40

48


16

tbw

g

lc

p cc

ct p

lt

lp

64

72


beam

80

n

A.7 – 9



Q3 =



0.76979927E+04

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1330E+03 0.1189E+03 0.1319E+03 0.1874E+03 3 0.40 55.70 47.55 59.35 73.98 0.1720E+03 0.1186E+03 0.1579E+03 0.1811E+03 5 0.90 134.00 106.56 137.85 160.96 0.1460E+03 0.1173E+03 0.1518E+03 0.1661E+03 7 1.45 216.50 170.28 215.28 246.97 0.1340E+03 0.1140E+03 0.1288E+03 0.1464E+03 9 2.05 284.50 236.77 284.69 328.33 0.9857E+02 0.1071E+03 0.1034E+03 0.1250E+03 11 2.90 357.00 321.79 360.94 422.74 0.7601E+02 0.9222E+02 0.7833E+02 0.9805E+02 13 3.90 429.00 404.29 430.83 507.79 0.6799E+02 0.7308E+02 0.6343E+02 0.7327E+02 15 5.00 497.50 474.97 495.97 576.97 0.5750E+02 0.5637E+02 0.5580E+02 0.5368E+02 17 6.40 570.50 543.28 569.11 639.59 0.4813E+02 0.4233E+02 0.4862E+02 0.3705E+02 19 8.75 658.50 625.77 666.64 706.04 0.3194E+02 0.2931E+02 0.3391E+02 0.2134E+02 21 12.20 754.00 709.08 747.26 759.05 0.2165E+02 0.2016E+02 0.1424E+02 0.1092E+02 23 15.53 818.67 767.91 819.59 787.09 0.1940E+02 0.1557E+02 0.1757E+02 0.6433E+01 25 19.43 880.00 821.89 879.46 806.55 0.1298E+02 0.1237E+02 0.1401E+02 0.3846E+01 27 23.90 938.00 871.65 940.28 820.02 0.1280E+02 0.1008E+02 0.1346E+02 0.2354E+01 29 26.50 971.00 896.55 975.29 825.43 0.1424E+02 0.9118E+01 0.1347E+02 0.1835E+01 31 30.10 1030.00 927.41 1023.79 831.09 0.1433E+02 0.8074E+01 0.1346E+02 0.1345E+01 33 33.30 1070.00 952.04 1066.78 834.90 0.2635E+02 0.7342E+01 0.1340E+02 0.1049E+01 35 35.30 1140.00 966.52 1156.39 836.85 0.5028E+02 0.6948E+01 0.4478E+02 0.9078E+00 37 36.90 1240.00 977.28 1228.00 838.22 0.5417E+02 0.6672E+01 0.4473E+02 0.8132E+00 39 39.30 1340.00 992.78 1335.29 840.03 0.4123E+02 0.6297E+01 0.4467E+02 0.6951E+00 41 42.00 1450.00 1009.27 1455.82 841.76 0.7230E+01 0.5925E+01 0.4461E+02 0.5888E+00 43 45.00 1360.00 1026.49 1359.23 843.38 -0.1029E+03 0.5565E+01 -0.3222E+02 0.4953E+00 45 45.85 1255.00 1031.20 1254.74 843.79 -0.1235E+03 0.5471E+01 -0.1229E+03 0.4726E+00 47 46.70 1150.00 1035.83 1150.25 844.18 -0.1235E+03 0.5381E+01 -0.1229E+03 0.4513E+00 ----------------------------------------------------------------------------------------------------------------------------





A.7 – 10


: :


1) 2)

1.5000" 4.0000"

p = lp =

3.0000" 9.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 7.3750" tbw= 0.3350" n = 2 X 3


Major parameters



Tested by Test Id.

VII -

6

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

9

27

36

45

54


18

tbw

g

lc

p cc

ct p

lt

lp

72

81


beam

90

n

A.7 – 11



Q3 =



0.19263089E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.4050E+02 0.4026E+02 0.3614E+02 0.5733E+02 3 1.60 63.00 63.41 64.18 75.85 0.3972E+02 0.3812E+02 0.3915E+02 0.3912E+02 5 2.90 111.00 108.96 110.62 120.35 0.3210E+02 0.3122E+02 0.3218E+02 0.2994E+02 7 5.70 184.00 173.24 183.16 186.31 0.2159E+02 0.1642E+02 0.2077E+02 0.1853E+02 9 8.60 232.00 210.39 232.41 230.28 0.1367E+02 0.1012E+02 0.1365E+02 0.1241E+02 11 12.10 268.50 239.40 269.41 265.88 0.8336E+01 0.6889E+01 0.7992E+01 0.8338E+01 13 15.90 293.00 261.93 293.31 292.38 0.5217E+01 0.5145E+01 0.5094E+01 0.5829E+01 15 21.00 317.00 284.60 316.77 316.73 0.4286E+01 0.3876E+01 0.4464E+01 0.3913E+01 17 25.10 358.00 299.13 354.87 330.74 0.1854E+02 0.3253E+01 0.1958E+02 0.2983E+01 19 28.20 426.00 308.66 415.52 339.18 0.8822E+02 0.2909E+01 0.1951E+02 0.2483E+01 21 28.90 498.00 310.69 505.66 340.88 0.1167E+03 0.2841E+01 0.1287E+03 0.2387E+01 23 29.80 619.00 313.22 621.49 342.98 0.1344E+03 0.2759E+01 0.1287E+03 0.2272E+01 25 30.70 740.00 315.69 737.24 344.97 0.1326E+03 0.2682E+01 0.1286E+03 0.2165E+01 27 31.57 853.33 318.00 848.62 346.81 0.1308E+03 0.2612E+01 0.1285E+03 0.2070E+01 29 32.45 960.00 320.29 962.04 348.60 0.1111E+03 0.2545E+01 0.1283E+03 0.1978E+01 31 33.90 1055.00 323.83 1056.08 351.36 0.4500E+02 0.2445E+01 0.3623E+02 0.1841E+01 33 36.70 1150.00 330.43 1156.85 356.19 0.2407E+02 0.2271E+01 0.3574E+02 0.1613E+01 35 41.05 1225.00 339.87 1223.31 362.57 0.1515E+02 0.2047E+01 0.1488E+02 0.1335E+01 37 44.55 1275.00 346.78 1274.34 366.92 0.1351E+02 0.1900E+01 0.1429E+02 0.1160E+01 39 49.06 1302.00 354.92 1303.52 371.73 0.7525E+00 0.1743E+01 0.9582E+00 0.9806E+00 41 54.38 1306.00 363.77 1307.11 376.50 0.7525E+00 0.1589E+01 0.4260E+00 0.8179E+00 43 59.70 1310.00 371.96 1308.38 380.50 0.7525E+00 0.1462E+01 0.7904E-01 0.6926E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.64750000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.15878415E+03 0.25934010E+04 -0.15980889E+05 0.41666718E+05 -0.46956736E+05 Rj0 = 23.8000 28.2000 32.9000 36.7000 46.4000 RKj = 0.14957917E+02 0.10927286E+03 -0.91880402E+02 -0.20061223E+02 -0.12711962E+02



A.7 – 12


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 12.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 4.3750" tbw= 0.3350" n = 2 X 4


Major parameters



Tested by Test Id.

VII -

7

0

200

400

600

800

1000

1200

1400

1600

1800

2000

tp

column

Moment ( kip-inch )


0

12

36

48

60

72


24

tbw

g

lc

p cc

ct p

lt

lp

96

n

108 120


beam

A.7 – 13



Q3 =



-0.40463083E+04

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1890E+03 0.7802E+02 0.1446E+03 0.1313E+03 3 0.50 69.20 38.96 67.66 60.09 0.1219E+03 0.7773E+02 0.1261E+03 0.1102E+03 5 1.20 147.00 92.88 147.44 129.26 0.1010E+03 0.7598E+02 0.1024E+03 0.8870E+02 7 2.20 232.50 165.80 235.37 206.72 0.7699E+02 0.6879E+02 0.7482E+02 0.6768E+02 9 3.60 319.00 250.43 320.25 287.31 0.4943E+02 0.5155E+02 0.4859E+02 0.4898E+02 11 6.80 426.00 367.21 424.24 404.37 0.1981E+02 0.2586E+02 0.2151E+02 0.2735E+02 13 11.00 484.00 448.54 485.51 490.77 0.1221E+02 0.1483E+02 0.9449E+01 0.1548E+02 15 16.85 534.00 516.83 535.66 558.19 0.7119E+01 0.9387E+01 0.8600E+01 0.8586E+01 17 22.55 572.50 562.80 574.10 597.41 0.6364E+01 0.7001E+01 0.5477E+01 0.5515E+01 19 27.90 602.67 596.49 601.20 622.30 0.4871E+01 0.5695E+01 0.4902E+01 0.3923E+01 21 33.10 628.00 623.77 627.34 640.00 0.4998E+01 0.4845E+01 0.5224E+01 0.2956E+01 23 39.57 661.33 652.57 663.18 656.43 0.5155E+01 0.4106E+01 0.5857E+01 0.2183E+01 25 44.85 691.50 673.04 695.30 666.77 0.6585E+01 0.3663E+01 0.6280E+01 0.1757E+01 27 47.40 774.00 682.31 748.85 671.04 0.1091E+03 0.3481E+01 0.8109E+02 0.1594E+01 29 49.20 879.00 688.35 894.90 673.82 0.6293E+02 0.3369E+01 0.8118E+02 0.1493E+01 31 50.60 986.00 693.04 1008.60 675.86 0.9837E+02 0.3284E+01 0.8125E+02 0.1421E+01 33 51.80 1120.00 696.96 1106.12 677.53 0.8950E+02 0.3216E+01 0.8129E+02 0.1363E+01 35 54.53 1226.67 705.47 1216.79 681.09 0.3903E+02 0.3073E+01 0.4053E+02 0.1244E+01 37 57.57 1343.34 714.67 1339.86 684.68 0.3800E+02 0.2927E+01 0.4061E+02 0.1129E+01 39 60.90 1470.00 724.08 1475.34 688.26 0.2791E+02 0.2786E+01 0.4067E+02 0.1021E+01 41 66.90 1533.33 740.12 1535.46 693.88 0.1075E+02 0.2565E+01 0.1005E+02 0.8611E+00 43 73.10 1600.00 755.41 1597.92 698.81 -0.4194E+01 0.2373E+01 0.1009E+02 0.7326E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.66250000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.10210273E+03 0.13972597E+04 -0.26474650E+04 -0.43917684E+03 0.63086274E+04 Rj0 = 13.9000 46.9000 51.8000 60.9000 73.1000 RKj = 0.70187684E+01 0.74651519E+02 -0.40853784E+02 -0.30690343E+02 -0.30071595E+02



A.7 – 14


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 15.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 1.3750" tbw= 0.3350" n = 2 X 5


Major parameters



Tested by Test Id.

VII -

8

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

9

27

36

45

54


18

tbw

g

lc

p cc

ct p

lt

lp

72

81


beam

90

n

A.7 – 15



Q3 =



0.19897490E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.9450E+02 0.1304E+03 0.1762E+03 0.2524E+03 3 0.30 45.50 39.10 49.78 69.63 0.2240E+03 0.1302E+03 0.1565E+03 0.2145E+03 5 0.60 93.80 78.12 94.31 129.61 0.1575E+03 0.1296E+03 0.1410E+03 0.1865E+03 7 0.90 140.00 116.83 134.73 182.11 0.1394E+03 0.1286E+03 0.1289E+03 0.1643E+03 9 1.30 188.00 167.84 183.67 242.90 0.1125E+03 0.1262E+03 0.1164E+03 0.1407E+03 11 2.10 266.00 265.42 269.46 341.07 0.1004E+03 0.1166E+03 0.9941E+02 0.1071E+03 13 2.80 338.00 342.56 335.30 408.66 0.9161E+02 0.1032E+03 0.8916E+02 0.8704E+02 15 3.60 401.00 418.29 402.75 471.30 0.7751E+02 0.8614E+02 0.7972E+02 0.7046E+02 17 4.47 467.00 485.65 467.87 526.43 0.7615E+02 0.6990E+02 0.7066E+02 0.5744E+02 19 5.63 541.34 557.27 543.63 585.74 0.5636E+02 0.5391E+02 0.5939E+02 0.4502E+02 21 7.10 624.00 626.14 621.21 643.51 0.4945E+02 0.4105E+02 0.4671E+02 0.3447E+02 23 8.50 684.00 677.77 679.29 686.67 0.3789E+02 0.3324E+02 0.3661E+02 0.2756E+02 25 11.40 764.00 758.99 762.86 752.31 0.2294E+02 0.2382E+02 0.2247E+02 0.1860E+02 27 15.73 833.33 845.27 836.99 816.08 0.1600E+02 0.1684E+02 0.1339E+02 0.1165E+02 29 20.40 891.50 913.84 889.87 860.54 0.9401E+01 0.1292E+02 0.9693E+01 0.7794E+01 31 25.40 938.50 971.68 937.71 893.18 0.9401E+01 0.1041E+02 0.9496E+01 0.5472E+01 33 29.93 974.00 1015.18 975.52 914.79 0.5926E+01 0.8901E+01 0.7279E+01 0.4168E+01 35 33.98 998.00 1049.11 1001.64 929.95 0.5926E+01 0.7899E+01 0.5692E+01 0.3362E+01 37 38.65 1025.00 1083.87 1025.01 944.02 0.5660E+01 0.7010E+01 0.4396E+01 0.2694E+01 39 43.53 1030.00 1116.27 1028.05 955.88 -0.4478E+01 0.6287E+01 -0.3693E+01 0.2191E+01 41 48.00 1010.00 1143.12 1010.48 964.86 -0.1692E+02 0.5755E+01 -0.4136E+01 0.1845E+01 43 50.90 937.50 1159.59 937.80 969.94 -0.2500E+02 0.5456E+01 -0.2514E+02 0.1663E+01 45 53.80 865.00 1174.92 864.70 974.53 -0.2500E+02 0.5194E+01 -0.2527E+02 0.1507E+01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.49833333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 3 AI = 0.22527156E+02 0.18216926E+04 -0.14458024E+05 0.40049489E+05 -0.46335194E+05 Rj0 = 22.9000 41.3000 48.0000 RKj = 0.25810032E+01 -0.72522892E+01 -0.20829964E+02



A.7 – 16


: :


1) 2)

1.5000" 4.0000"

p = lp =

3.0000" 9.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 13.3750" tbw= 0.4410" n = 2 X 3


Major parameters



Tested by Test Id.

VII -

9

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

9

27

36

45

54


18

tbw

g

lc

p cc

ct p

lt

lp

72

81


beam

90

n

A.7 – 17



Q3 =



0.65573976E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2650E+02 0.4619E+02 0.1403E+03 0.8284E+02 3 2.80 74.20 121.46 68.83 138.00 0.2543E+02 0.3657E+02 0.2128E+02 0.3130E+02 5 7.30 170.00 224.74 178.92 230.02 0.2007E+02 0.1408E+02 0.2105E+02 0.1353E+02 7 11.77 250.00 272.02 248.75 275.72 0.1477E+02 0.8147E+01 0.1247E+02 0.7767E+01 9 16.10 314.00 301.69 304.70 303.12 0.1268E+02 0.5827E+01 0.1393E+02 0.5154E+01 11 21.65 369.50 329.38 380.96 326.32 0.1000E+02 0.4315E+01 0.1169E+02 0.3397E+01 13 27.20 425.00 350.75 413.14 342.23 0.1724E+03 0.3454E+01 -0.1611E+01 0.2421E+01 15 27.65 566.00 352.30 594.43 343.31 0.5600E+03 0.3400E+01 0.3353E+03 0.2362E+01 17 28.20 746.00 354.16 778.35 344.58 0.4000E+03 0.3337E+01 0.3335E+03 0.2292E+01 19 28.55 914.00 355.33 894.88 345.38 0.4800E+03 0.3297E+01 0.3324E+03 0.2249E+01 21 29.10 1080.00 357.13 1077.18 346.60 0.4277E+03 0.3238E+01 0.3305E+03 0.2185E+01 23 29.40 1230.00 358.10 1176.19 347.25 0.4143E+03 0.3206E+01 0.3295E+03 0.2151E+01 25 29.80 1350.00 359.38 1307.72 348.10 0.2733E+03 0.3165E+01 0.3282E+03 0.2107E+01 27 30.30 1470.00 360.96 1471.37 349.14 0.2218E+03 0.3116E+01 0.3264E+03 0.2053E+01 29 30.90 1590.00 362.82 1666.62 350.35 0.1733E+03 0.3058E+01 0.3244E+03 0.1992E+01 31 31.80 1710.00 365.55 1705.73 352.11 0.1106E+03 0.2976E+01 0.4189E+02 0.1906E+01 33 33.80 1830.00 371.31 1817.37 355.74 0.5338E+02 0.2812E+01 0.5237E+02 0.1733E+01 35 36.50 1950.00 378.66 1946.52 360.15 0.3823E+02 0.2617E+01 0.4339E+02 0.1535E+01 37 40.70 2070.00 389.05 2078.18 366.06 0.2565E+02 0.2369E+01 0.2528E+02 0.1291E+01 39 46.20 2190.00 401.34 2179.77 372.46 0.1542E+02 0.2111E+01 0.1232E+02 0.1051E+01 41 50.87 2236.66 410.77 2237.75 377.00 0.9999E+01 0.1936E+01 0.8613E+01 0.8979E+00 43 55.60 2260.00 419.58 2263.84 380.94 0.0000E+00 0.1788E+01 0.2751E+01 0.7750E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.81333333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.91988861E+03 -0.11767422E+05 0.37326682E+05 -0.11421234E+05 -0.76619509E+05 Rj0 = 0.0000 27.2000 27.5000 30.9000 31.8000 36.5000 46.2000 RKj = -0.84499326E+02 0.43863262E+03 -0.10032418E+03 -0.27934745E+03 0.17398218E+02 -0.56205905E+01 0.43335297E+01



A.7 – 18


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 12.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 10.3750" tbw= 0.4400" n = 2 X 4


Major parameters



Tested by Test Id.

VII - 10

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

9

27

36

45

54


18

tbw

g

lc

p cc

ct p

lt

lp

72

81


beam

90

n

A.7 – 19



Q3 =



-0.23245794E+06

-10



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10358333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.19194058E+04 -0.41285920E+05 0.24290916E+06 -0.58371541E+06 0.61282114E+06 Rj0 = 16.2000 31.2000 32.0000 37.5000 39.8000 44.4000 RKj = -0.10158346E+02 0.96703066E+02 0.16058581E+03 -0.17233594E+03 -0.21320413E+02 -0.15610711E+02



A.7 – 20


: :


1) 2)

1.5000" 5.5000"

p = 3.0000" lp = 15.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 7.3750" tbw= 0.4410" n = 2 X 5


Major parameters



Tested by Test Id.

VII - 11

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

12

36

48

60

72


24

tbw

g

lc

p cc

ct p

lt

lp

96

n

108 120


beam

A.7 – 21



Q3 =



-0.66837979E+04

-10



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.77666667E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.40147681E+03 -0.68148987E+04 0.28713136E+05 -0.46715239E+05 0.31939556E+05 Rj0 = 38.5000 40.8000 48.1000 51.5000 62.8000 68.8000 RKj = 0.45047140E+01 0.10968022E+03 -0.56700154E+02 -0.28634717E+02 -0.10003982E+02 -0.92912071E+01



A.7 – 22


: :


1) 2)

1.5000" 5.5000"

p = 3.0000" lp = 18.0000"

1.5000" 0.3750"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 4.3750" tbw= 0.4410" n = 2 X 6


Major parameters



Tested by Test Id.

VII - 12

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

13

39

52

65

78

91

lc

p cc

ct p

lt

lp

n


26

tbw

g


beam

A.7 – 23



Q3 =



0.19356713E+05

-10



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.81750000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.53478411E+03 0.71574712E+04 -0.29266073E+05 0.58584976E+05 -0.54163971E+05 Rj0 = 19.3000 53.3000 54.7000 68.4000 73.9000 RKj = 0.79784484E+01 0.69763028E+02 -0.13527065E+02 -0.38029441E+02 -0.11188505E+02



A.7 – 24


: :


1) 2)

1.5000" 5.5000"

p = 3.0000" lp = 18.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 10.3750" tbw= 0.4410" n = 2 X 4


Major parameters



Tested by Test Id.

VII - 13

0

150

300

450

600

750

900

1050

1200

1350

1500

tp

column

Moment ( kip-inch )


0

10

30

40

50

60


20

tbw

g

lc

p cc

ct p

lt

lp

80

90


beam

100

n

A.7 – 25



Q3 =



-0.36641019E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1860E+02 0.7143E+02 0.3092E+02 0.2886E+02 3 4.10 74.40 251.46 74.62 76.98 0.2133E+02 0.4183E+02 0.2077E+02 0.1440E+02 5 6.20 123.00 321.25 122.54 104.67 0.1919E+02 0.2640E+02 0.2407E+02 0.1213E+02 7 12.00 171.00 423.53 170.07 163.44 0.6732E+01 0.1234E+02 0.6253E+01 0.8569E+01 9 16.60 196.34 470.99 196.05 198.92 0.5508E+01 0.8730E+01 0.5505E+01 0.6966E+01 11 21.55 223.50 508.71 223.97 230.31 0.5470E+01 0.6703E+01 0.5591E+01 0.5789E+01 13 25.60 258.00 533.62 244.37 252.26 0.1962E+02 0.5663E+01 0.4213E+01 0.5077E+01 15 27.65 320.50 544.83 331.35 262.35 0.4454E+02 0.5258E+01 0.4177E+02 0.4776E+01 17 28.60 369.00 549.79 370.71 266.83 0.6000E+02 0.5090E+01 0.4108E+02 0.4647E+01 19 29.35 426.50 553.58 421.34 270.28 0.9571E+02 0.4965E+01 0.9777E+02 0.4550E+01 21 30.03 492.33 556.95 487.96 273.36 0.9700E+02 0.4858E+01 0.9721E+02 0.4465E+01 23 30.70 557.00 560.18 552.58 276.31 0.9237E+02 0.4757E+01 0.9665E+02 0.4385E+01 25 31.43 621.00 563.65 623.23 279.49 0.8728E+02 0.4652E+01 0.9602E+02 0.4300E+01 27 33.17 689.25 571.41 693.97 286.81 0.2636E+02 0.4426E+01 0.2527E+02 0.4109E+01 29 35.92 761.75 583.14 760.07 297.73 0.2636E+02 0.4110E+01 0.2282E+02 0.3837E+01 31 39.13 830.33 595.81 828.88 309.58 0.1764E+02 0.3798E+01 0.2012E+02 0.3559E+01 33 42.80 895.00 609.17 897.61 322.12 0.1725E+02 0.3499E+01 0.1746E+02 0.3284E+01 35 46.60 959.00 621.96 959.59 334.11 0.1684E+02 0.3239E+01 0.1526E+02 0.3036E+01 37 50.45 1010.50 633.99 1010.26 345.37 0.1000E+02 0.3016E+01 0.1118E+02 0.2817E+01 39 55.20 1060.00 647.75 1059.98 358.18 0.1005E+02 0.2783E+01 0.9868E+01 0.2584E+01 41 58.30 1090.00 656.27 1089.70 365.98 -0.8416E+02 0.2649E+01 0.9340E+01 0.2449E+01 43 59.03 1012.00 658.21 1011.89 367.77 -0.1064E+03 0.2620E+01 -0.1062E+03 0.2419E+01 45 59.77 934.00 660.12 934.00 369.53 -0.1064E+03 0.2592E+01 -0.1062E+03 0.2389E+01 47 60.50 856.00 662.02 856.06 371.27 -0.1064E+03 0.2564E+01 -0.1063E+03 0.2361E+01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10041667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.64660258E+03 -0.10511079E+05 0.54982919E+05 -0.12001572E+06 0.11227076E+06 Rj0 = 6.2000 25.6000 29.0000 31.8000 48.5000 58.3000 RKj = -0.14695233E+02 0.38823165E+02 0.57270527E+02 -0.69213921E+02 -0.24490542E+01 -0.11540635E+03



A.7 – 26


: :


1) 2)

1.5000" 5.5000"

p = 3.0000" lp = 15.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 7.3750" tbw= 0.4410" n = 2 X 5


Major parameters



Tested by Test Id.

VII - 14

0

250

500

750

1000

1250

1500

1750

2000

2250

2500

tp

column

Moment ( kip-inch )


0

16

48

64

80

96

lc

p cc

ct p

lt

lp

n


32

tbw

g


beam

A.7 – 27



Q3 =



-0.20453469E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2657E+02 0.4697E+02 0.1560E+02 0.1710E+02 3 4.60 123.00 178.29 124.01 78.42 0.2509E+02 0.2441E+02 0.2575E+02 0.1691E+02 5 11.50 238.00 274.34 237.64 190.88 0.1130E+02 0.8496E+01 0.1015E+02 0.1543E+02 7 20.30 316.00 328.84 313.57 311.45 0.7846E+01 0.4675E+01 0.8215E+01 0.1177E+02 9 27.10 364.00 356.28 365.46 380.91 0.9677E+01 0.3525E+01 0.6672E+01 0.8711E+01 11 30.50 431.00 367.64 431.09 408.18 0.4588E+02 0.3148E+01 0.6812E+02 0.7360E+01 13 31.85 508.50 371.85 522.60 417.79 0.6467E+02 0.3021E+01 0.6745E+02 0.6869E+01 15 33.35 605.00 376.23 623.20 427.70 0.6400E+02 0.2895E+01 0.6669E+02 0.6357E+01 17 34.80 701.50 380.38 695.62 436.58 0.6928E+02 0.2782E+01 0.3203E+02 0.5894E+01 19 38.10 822.50 389.12 798.54 454.44 0.2788E+02 0.2559E+01 0.3037E+02 0.4954E+01 21 43.65 967.50 402.46 960.15 478.28 0.2458E+02 0.2260E+01 0.2797E+02 0.3701E+01 23 50.40 1110.00 416.74 1141.59 499.37 0.2658E+02 0.1985E+01 0.2597E+02 0.2619E+01 25 54.30 1230.00 424.22 1241.43 508.66 0.3039E+02 0.1857E+01 0.2528E+02 0.2160E+01 27 58.30 1350.00 431.42 1341.68 516.52 0.2752E+02 0.1743E+01 0.2488E+02 0.1783E+01 29 63.20 1470.00 439.66 1463.07 524.33 0.2669E+02 0.1623E+01 0.2472E+02 0.1423E+01 31 67.40 1590.00 446.37 1567.00 529.78 0.2468E+02 0.1533E+01 0.2479E+02 0.1182E+01 33 73.80 1710.00 455.80 1726.70 536.40 0.1202E+02 0.1416E+01 0.2515E+02 0.9029E+00 35 81.55 1740.00 466.22 1745.59 542.42 0.3871E+01 0.1299E+01 0.2755E+01 0.6656E+00 37 89.30 1770.00 475.90 1769.49 546.91 -0.1724E+01 0.1201E+01 0.3409E+01 0.5012E+00 39 97.85 1685.00 485.84 1682.54 550.62 -0.1169E+02 0.1110E+01 -0.9852E+01 0.3747E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.15475000E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 5 AI = -0.69527770E+03 0.59813648E+04 -0.11571189E+05 -0.73209794E+04 0.34245539E+05 Rj0 = 27.1000 29.6000 34.1000 73.8000 89.3000 RKj = -0.45031286E+01 0.67440657E+02 -0.33916964E+02 -0.23008050E+02 -0.13914523E+02



A.7 – 28


: :


1) 2)

1.5000" 5.5000"

p = 3.0000" lp = 12.0000"

1.5000" 0.5000"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 10.3750" tbw= 0.4410" n = 2 X 4


Major parameters



Tested by Test Id.

VII - 15

0

350

700

1050

1400

1750

2100

2450

2800

3150

3500

tp

column

Moment ( kip-inch )


0

13

39

52

65

78

91

lc

p cc

ct p

lt

lp

n


26

tbw

g


beam

A.7 – 29



Q3 =



-0.62974380E+05

-10



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.12283333E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.91769952E+03 -0.13475908E+05 0.70214852E+05 -0.16072370E+06 0.16648437E+06 Rj0 = 28.7000 45.7000 47.9000 53.4000 58.4000 67.4000 RKj = 0.33342312E+01 0.57812256E+02 0.15461777E+03 -0.15974602E+03 -0.30630493E+02 -0.17234306E+02



A.7 – 30


: :


1) 2)

1.5000" 5.5000"

p = 3.0000" lp = 15.0000"

1.5000" 0.5000"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 7.3750" tbw= 0.4410" n = 2 X 5


Major parameters



Tested by Test Id.

VII - 16

0

300

600

900

1200

1500

1800

2100

2400

2700

3000

tp

column

Moment ( kip-inch )


0

11

33

44

55

66


22

tbw

g

lc

p cc

ct p

lt

lp

88

99


beam

110

n

A.7 – 31



Q3 =



0.49851587E+05

-10



Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.68083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.60325610E+03 0.77747393E+04 -0.42099725E+05 0.10714682E+06 -0.12084964E+06 Rj0 = 19.2000 47.5000 48.9000 56.0000 RKj = -0.29379514E+01 0.80848854E+02 0.54703670E+02 -0.12539968E+03



A.7 – 32


: :


1) 2)

1.5000" 4.0000"

p = 3.0000" lp = 12.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 4.3750" tbw= 0.3350" n = 2 X 4


Major parameters



Tested by Test Id.

VII - 17

0

100

200

300

400

500

600

700

800

900

1000

tp

column

Moment ( kip-inch )


0

12

36

48

60

72


24

tbw

g

lc

p cc

ct p

lt

lp

96

n

108 120


beam

A.7 – 33



Q3 =



0.37668683E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3365E+02 0.4078E+02 0.3692E+02 0.3891E+02 3 1.70 57.20 68.08 55.69 65.90 0.3015E+02 0.3826E+02 0.2994E+02 0.3838E+02 5 3.20 97.80 119.57 98.11 122.12 0.2587E+02 0.2961E+02 0.2665E+02 0.3628E+02 7 6.00 164.00 180.31 163.04 213.26 0.2016E+02 0.1567E+02 0.1947E+02 0.2809E+02 9 8.90 212.00 216.12 208.42 279.90 0.1372E+02 0.9859E+01 0.1214E+02 0.1809E+02 11 15.55 260.00 263.53 260.50 349.96 0.7218E+01 0.5332E+01 0.6069E+01 0.5428E+01 13 22.20 308.00 292.89 309.42 371.81 0.5873E+01 0.3716E+01 0.9117E+01 0.1875E+01 15 29.47 340.00 316.33 338.98 380.51 0.4404E+01 0.2826E+01 0.5033E+01 0.7358E+00 17 36.03 369.00 333.18 371.13 383.96 0.4432E+01 0.2340E+01 0.4370E+01 0.3686E+00 19 41.90 395.00 345.98 391.40 385.63 0.5707E+01 0.2037E+01 0.2424E+01 0.2176E+00 21 48.60 443.00 358.72 448.47 386.76 0.3550E+02 0.1781E+01 0.7255E+01 0.1290E+00 23 50.00 501.00 361.20 496.58 386.93 0.3782E+02 0.1735E+01 0.3411E+02 0.1166E+00 25 52.00 566.34 364.64 564.12 387.15 0.3267E+02 0.1675E+01 0.3344E+02 0.1015E+00 27 54.00 630.67 367.96 630.35 387.34 0.3166E+02 0.1619E+01 0.3281E+02 0.8876E-01 29 56.00 694.00 371.08 695.39 387.51 0.2638E+02 0.1569E+01 0.3223E+02 0.7800E-01 31 61.67 758.67 379.68 760.09 387.88 0.1141E+02 0.1439E+01 0.1078E+02 0.5533E-01 33 67.00 801.34 387.05 801.06 388.13 0.4133E+01 0.1338E+01 0.4499E+01 0.4115E-01 35 72.00 822.00 393.53 821.96 388.32 -0.4284E+02 0.1256E+01 0.3897E+01 0.3182E-01 37 73.27 752.66 395.11 752.68 388.36 -0.5474E+02 0.1237E+01 -0.5476E+02 0.2990E-01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.82833333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 6 AI = 0.61227884E+02 0.54083011E+03 -0.14049795E+05 0.56916752E+05 -0.80472582E+05 Rj0 = 22.2000 41.9000 48.6000 56.0000 64.4000 72.0000 RKj = -0.65904242E+01 0.73764990E+01 0.27356308E+02 -0.20111445E+02 -0.53741093E+01 -0.58531294E+02



A.7 – 34


: :


1) 2)

1.5000" 4.0000"

p = lp =

3.0000" 9.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 7.3750" tbw= 0.3350" n = 2 X 3


Major parameters



Tested by Test Id.

VII - 18

0

80

160

240

320

400

480

560

640

720

800

tp

column

Moment ( kip-inch )


0

10

30

40

50

60


20

tbw

g

lc

p cc

ct p

lt

lp

80

90


beam

100

n

A.7 – 35



Q3 =



0.44587137E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2825E+02 0.2104E+02 0.2292E+02 0.1699E+02 3 1.20 33.90 25.05 34.67 20.39 0.2721E+02 0.2049E+02 0.2883E+02 0.1699E+02 5 2.50 67.80 50.15 65.39 42.47 0.2259E+02 0.1766E+02 0.1823E+02 0.1699E+02 7 7.10 115.00 101.08 113.75 120.04 0.7180E+01 0.6628E+01 0.9321E+01 0.1644E+02 9 12.74 134.20 127.41 135.02 193.75 0.3404E+01 0.3401E+01 0.3586E+01 0.7864E+01 11 18.38 153.40 143.09 152.97 214.78 0.3404E+01 0.2316E+01 0.3219E+01 0.1257E+01 13 23.90 188.00 154.27 188.20 218.01 0.1999E+02 0.1784E+01 0.9641E+01 0.2244E+00 15 25.43 223.33 156.96 222.97 218.29 0.2304E+02 0.1677E+01 0.2275E+02 0.1469E+00 17 26.60 265.00 158.84 266.72 218.44 0.6000E+02 0.1608E+01 0.6573E+02 0.1080E+00 19 27.30 311.33 159.96 312.73 218.51 0.7445E+02 0.1568E+01 0.6571E+02 0.9035E-01 21 27.90 356.00 160.90 352.14 218.56 0.6905E+02 0.1535E+01 0.6567E+02 0.7779E-01 23 28.58 398.80 161.93 396.78 218.61 0.6294E+02 0.1500E+01 0.6560E+02 0.6589E-01 25 29.26 441.60 162.95 441.35 218.65 0.6294E+02 0.1467E+01 0.6550E+02 0.5602E-01 27 31.43 485.50 166.00 487.86 218.75 0.1227E+02 0.1372E+01 0.1300E+02 0.3413E-01 29 35.10 530.50 170.78 533.40 218.83 0.1227E+02 0.1237E+01 0.1177E+02 0.1588E-01 31 38.77 575.50 175.11 573.82 218.87 0.1227E+02 0.1129E+01 0.1026E+02 0.7966E-02 33 42.65 612.00 179.30 610.50 218.90 0.6831E+01 0.1034E+01 0.8647E+01 0.4102E-02 35 47.73 639.00 184.29 642.03 218.91 0.4286E+01 0.9338E+00 0.4311E+01 0.1875E-02 37 53.80 665.00 189.66 662.95 218.92 0.1120E+01 0.8388E+00 0.2691E+01 0.8157E-03 39 58.93 657.00 193.79 657.31 218.92 -0.1558E+01 0.7735E+00 -0.1526E+01 0.4327E-03 41 61.67 631.17 195.90 631.13 218.92 -0.1310E+03 0.7426E+00 -0.1309E+03 0.3156E-03 43 62.00 587.50 196.15 587.49 218.92 -0.1310E+03 0.7391E+00 -0.1309E+03 0.3040E-03 45 62.33 543.83 196.40 543.85 218.92 -0.1310E+03 0.7356E+00 -0.1310E+03 0.2929E-03 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.67083333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 8 AI = -0.39740207E+03 0.67064618E+04 -0.37889702E+05 0.95407775E+05 -0.10789154E+06 Rj0 = 7.1000 21.2000 23.9000 26.2000 29.6000 44.7000 53.8000 61.5000 RKj = -0.63984496E+01 0.52996691E+01 0.12943555E+02 0.42948403E+02 -0.52021011E+02 -0.24977707E+01 -0.33018806E+01 -0.12902662E+03



A.7 – 36


: :


1) 2)

1.5000" 4.0000"

p = lp =

3.0000" 9.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 1.5000" tbw= 0.2390" n = 2 X 3


Major parameters



Tested by Test Id.

VII - 19

0

45

90

135

180

225

270

315

360

405

450

tp

column

Moment ( kip-inch )


0

16

48

64

80

96

lc

p cc

ct p

lt

lp

n


32

tbw

g


beam

A.7 – 37



Q3 =



0.16736052E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1631E+02 0.1777E+02 0.1495E+02 0.1247E+02 3 1.27 20.66 22.31 20.74 15.80 0.1631E+02 0.1724E+02 0.1684E+02 0.1247E+02 5 2.57 41.33 43.35 41.76 32.00 0.1550E+02 0.1473E+02 0.1523E+02 0.1246E+02 7 3.90 62.00 60.44 60.50 48.58 0.1354E+02 0.1092E+02 0.1288E+02 0.1240E+02 9 6.30 86.00 80.59 87.20 78.02 0.1000E+02 0.6444E+01 0.9658E+01 0.1207E+02 11 8.70 110.00 93.32 108.09 106.13 0.8383E+01 0.4412E+01 0.7941E+01 0.1126E+02 13 14.57 136.00 112.48 136.80 161.28 0.4432E+01 0.2489E+01 0.4036E+01 0.7195E+01 15 21.47 155.34 126.45 155.98 194.27 0.1596E+01 0.1674E+01 0.1787E+01 0.2834E+01 17 29.40 168.00 137.79 167.19 207.54 0.4370E+01 0.1234E+01 0.1176E+01 0.8993E+00 19 33.80 194.00 142.86 194.07 210.54 0.5909E+01 0.1082E+01 0.6042E+01 0.5044E+00 21 38.05 219.00 147.22 219.43 212.21 0.5854E+01 0.9697E+00 0.5882E+01 0.3027E+00 23 42.15 243.00 151.01 243.11 213.20 0.5854E+01 0.8829E+00 0.5654E+01 0.1928E+00 25 45.73 267.00 154.07 266.80 213.78 0.7869E+01 0.8196E+00 0.7971E+01 0.1340E+00 27 48.77 291.00 156.49 290.73 214.13 0.7869E+01 0.7732E+00 0.7714E+01 0.1002E+00 29 54.17 311.00 160.45 311.79 214.56 0.2069E+01 0.7042E+00 0.2253E+01 0.6229E-01 31 61.90 327.00 165.58 326.49 214.92 0.1666E+01 0.6256E+00 0.1562E+01 0.3388E-01 33 69.90 337.00 170.32 336.51 215.13 0.1160E+01 0.5622E+00 0.9679E+00 0.1941E-01 35 79.40 347.00 175.37 346.65 215.27 0.7958E+00 0.5031E+00 0.8354E+00 0.1080E-01 37 87.05 351.50 179.07 351.97 215.33 0.5882E+00 0.4646E+00 0.5735E+00 0.7074E-02 39 94.70 356.00 182.50 355.66 215.38 -0.6355E+01 0.4321E+00 0.4044E+00 0.4798E-02 41 97.42 332.00 183.67 331.90 215.39 -0.8824E+01 0.4217E+00 -0.8755E+01 0.4210E-02 43 100.14 308.00 184.81 308.04 215.40 -0.8824E+01 0.4118E+00 -0.8792E+01 0.3708E-02 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10041583E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = -0.13199049E+03 0.21143055E+04 -0.12495207E+05 0.33105212E+05 -0.38978570E+05 Rj0 = 8.7000 17.5000 29.4000 44.2000 50.3000 69.9000 94.7000 RKj = -0.19701924E+01 -0.86094578E+00 0.50023999E+01 0.25774885E+01 -0.49685056E+01 0.36808222E+00 -0.91162514E+01



A.7 – 38


: :


1) 2)

1.5000" 4.0000"

p = lp =

3.0000" 6.0000"

1.5000" 0.2500"

------------------------------


for beam web.

cc = tp =


ct = g =


Remark

lt = 1.5000" lc = 4.5000" tbw= 0.2390" n = 2 X 2


Major parameters



Tested by Test Id.

VII - 20

0

50

100

150

200

250

300

350

400

450

500

tp

column

Moment ( kip-inch )


0

19

57

76

95

lc

p cc

ct p

lt

lp

n


38

tbw

g


beam

A.7 – 39



Q3 =



-0.15465960E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.5482E+01 0.6995E+01 0.8332E+01 0.4129E+01 3 7.60 24.55 34.67 25.11 31.37 0.2127E+01 0.2031E+01 0.1920E+01 0.4124E+01 5 17.80 46.25 47.11 45.74 71.40 0.2127E+01 0.7957E+00 0.2216E+01 0.3356E+01 7 27.05 62.90 53.04 62.68 90.82 0.1398E+01 0.5259E+00 0.1284E+01 0.9383E+00 9 37.00 76.40 57.53 76.72 94.93 0.6313E+01 0.3916E+00 0.1381E+01 0.1366E+00 11 40.20 101.00 58.74 100.31 95.27 0.1190E+02 0.3628E+00 0.7283E+01 0.7730E-01 13 42.70 139.00 59.63 139.62 95.42 0.1535E+02 0.3431E+00 0.1563E+02 0.5076E-01 15 44.77 171.00 60.32 171.74 95.51 0.1548E+02 0.3289E+00 0.1545E+02 0.3642E-01 17 48.83 203.33 61.60 203.67 95.62 0.5385E+01 0.3041E+00 0.5126E+01 0.1970E-01 19 54.90 236.00 63.35 232.86 95.70 0.4672E+01 0.2738E+00 0.4495E+01 0.8563E-02 21 62.60 265.00 65.34 264.54 95.75 0.3293E+01 0.2438E+00 0.3759E+01 0.3354E-02 23 73.70 294.00 67.85 298.74 95.77 0.3854E+01 0.2113E+00 0.2740E+01 0.1043E-02 25 83.00 322.50 69.72 321.30 95.77 0.1793E+01 0.1905E+00 0.2184E+01 0.4454E-03 27 92.80 341.67 71.49 341.93 95.78 0.2148E+01 0.1731E+00 0.2057E+01 0.2002E-03 29 101.80 361.00 72.99 360.41 95.78 0.2107E+01 0.1598E+00 0.2063E+01 0.1032E-03 31 111.25 380.50 74.44 380.20 95.78 0.2063E+01 0.1482E+00 0.2132E+01 0.5461E-04 33 120.70 400.00 75.80 400.77 95.78 0.9832E+00 0.1382E+00 0.2223E+01 0.3045E-04 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.16666667E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 7 AI = 0.14372681E+03 -0.25211128E+04 0.15935685E+05 -0.39886547E+05 0.41910023E+05 Rj0 = 22.9000 37.0000 40.2000 45.8000 62.6000 77.7000 120.7000 RKj = -0.15481755E+01 0.60661482E+01 0.85276682E+01 -0.99331136E+01 -0.26941252E+00 -0.22780713E+00 -0.24252112E+01



A.7 – 40


: :


1) 2)

2.1654" 2.9920"

p = 3.9370" lp = 10.4331"

cc = tp =

2.3622" 0.4724"

------------------------------


Flush end plate welded to the web of the beam

ct = g =

Major parameters


Remark

lt = -" lc = -" tbw= 0.2284" n = 2 X 3

United Kingdom




Tested by Test Id.

VII - 21

0

45

90

135

180

225

270

315

360

405

450

tp

column

Moment ( kip-inch )


0

4

12

16

20

24

28

lc

p cc

ct p

lt

32


tbw

g


8

Material : : :

beam

36

lp

40

n

A.7 – 41



Q3 =


-10

-------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. Expri. Poly. M.Expo. -------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.1302E+03 0.1075E+03 0.1303E+03 3 0.19 24.58 20.29 28.65 0.1303E+03 0.1075E+03 0.1592E+03 5 0.32 49.16 34.06 49.45 0.3631E+03 0.1074E+03 0.1644E+03 7 0.38 73.75 41.33 60.60 0.3078E+03 0.1073E+03 0.1651E+03 9 0.64 98.33 68.81 102.14 0.9587E+02 0.1068E+03 0.1562E+03 11 0.83 122.91 89.34 130.76 0.1917E+03 0.1063E+03 0.1405E+03 13 0.96 147.49 102.95 147.95 0.1772E+03 0.1058E+03 0.1275E+03 15 1.12 172.07 119.21 166.26 0.1598E+03 0.1052E+03 0.1104E+03 17 1.44 196.66 152.51 195.81 0.5046E+02 0.1032E+03 0.7442E+02 19 1.92 221.24 201.70 220.69 0.4380E+02 0.9842E+02 0.5314E+02 21 2.88 250.74 289.70 250.72 0.2685E+02 0.8367E+02 0.2013E+02 23 3.85 272.86 362.00 272.87 0.1918E+02 0.6696E+02 0.2929E+02 25 5.29 293.14 443.73 292.57 0.1918E+02 0.4783E+02 0.1641E+02 27 6.25 311.58 485.43 310.32 0.1918E+02 0.3937E+02 0.1915E+02 29 7.69 331.86 535.59 334.27 0.1054E+02 0.3081E+02 0.1286E+02 31 9.62 350.29 587.51 347.93 0.6721E+01 0.2379E+02 0.2004E+01 33 11.54 357.70 628.73 358.46 0.3989E+01 0.1939E+02 0.3449E+01 35 13.46 365.64 662.96 364.18 0.3671E+01 0.1639E+02 0.3029E+01 37 15.20 368.73 689.71 370.44 -0.1119E+01 0.1440E+02 -0.4183E+01 39 16.35 366.52 705.53 366.23 -0.6065E+01 0.1335E+02 -0.3185E+01 41 18.27 350.30 729.77 350.22 -0.3843E+01 0.1191E+02 -0.2877E+01 43 20.18 345.13 751.46 345.75 -0.7821E+00 0.1077E+02 -0.1862E+01 45 21.72 331.86 767.51 331.86 -0.3198E+02 0.1001E+02 -0.2166E+02 --------------------------------------------------------------------------------------------------

Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.20788000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 10 AI = 0.21831906E+03 -0.72401627E+04 0.41315164E+05 -0.89287323E+05 0.84289152E+05 Rj0 = 0.0000 1.9200 3.8500 4.8100 9.6200 15.2000 16.3500 17.3100 21.1600 22.1100 RKj = 0.12609394E+02 0.22735295E+02 -0.23973084E+02 -0.87482334E+01 0.65473095E+01 -0.84818432E+01 -0.10676744E+02 0.95223851E+01 -0.20322708E+02 -0.17592468E+04



A.7 – 42


: :


1) 2)

1.5748" 3.9370"

p = lp =

2.7559" 5.9055"

cc = tp =

1.5748" 0.6299"

------------------------------


Failed with buckling of the compression flange of the beam Plate welded after coping the beam web

ct = g =


Remark

lt = 1.0472" lc = 1.0472" tbw= 0.2284" n = 2 X 2

P. New Guinea Fasteners: 10.9- -M20 7/8" Oversize holes Material : -Fy = 36.00 ksi Fu = -ksi

Major parameters

A.K.Aggarwal (1989) M 2


Tested by Test Id.

VII - 22

0

55

110

165

220

275

330

385

440

495

550

tp

column

Moment ( kip-inch )

Connection type : Header plate connections Mode : All bolted with column stiffener

0

16

48

64

80

96

lc

p cc

ct p

lt

lp

n


32

tbw

g


beam

A.7 – 43



Q3 =



-0.10708503E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3657E+02 0.2966E+02 0.6175E+02 0.6846E+02 3 1.03 37.51 30.26 44.56 67.08 0.3657E+02 0.2913E+02 0.2923E+02 0.5972E+02 5 2.05 75.02 59.11 68.43 119.55 0.3077E+02 0.2671E+02 0.1991E+02 0.4233E+02 7 3.90 112.52 100.85 106.22 173.61 0.1865E+02 0.1824E+02 0.2259E+02 0.1897E+02 9 6.15 150.03 132.91 162.35 201.20 0.3033E+02 0.1106E+02 0.2594E+02 0.7532E+01 11 7.18 187.54 143.23 188.60 207.65 0.3221E+02 0.9220E+01 0.2498E+02 0.5222E+01 13 8.62 225.05 155.11 222.34 213.63 0.2460E+02 0.7448E+01 0.2176E+02 0.3298E+01 15 10.26 262.56 166.15 254.12 217.95 0.1894E+02 0.6100E+01 0.1687E+02 0.2080E+01 17 14.36 300.10 186.84 299.72 223.38 0.6469E+01 0.4220E+01 0.6257E+01 0.8194E+00 19 20.51 315.07 208.30 317.09 226.45 0.2319E+01 0.2923E+01 0.1213E+01 0.2942E+00 21 27.35 330.07 225.59 328.12 227.78 0.2194E+01 0.2207E+01 0.2332E+01 0.1268E+00 23 35.90 354.45 242.12 353.85 228.51 0.3292E+01 0.1708E+01 0.3362E+01 0.5682E-01 25 46.15 384.45 257.68 386.32 228.92 0.2560E+01 0.1357E+01 0.2827E+01 0.2697E-01 27 54.36 408.84 268.02 407.09 229.09 0.1968E+01 0.1172E+01 0.2270E+01 0.1658E-01 29 61.54 408.84 275.97 408.66 229.19 -0.1416E-14 0.1049E+01 0.9806E-01 0.1146E-01 31 68.38 408.84 282.82 408.91 229.26 -0.4250E-14 0.9566E+00 -0.5334E-02 0.8373E-02 33 76.93 408.84 290.58 408.76 229.32 0.0000E+00 0.8631E+00 -0.1568E-01 0.5895E-02 35 85.47 408.84 297.68 408.77 229.36 -0.3008E-14 0.7873E+00 0.2305E-01 0.4306E-02 37 92.31 408.84 302.88 409.05 229.39 0.5852E+00 0.7368E+00 0.5862E-01 0.3423E-02 39 102.56 423.84 310.06 423.84 229.42 0.1463E+01 0.6735E+00 0.2250E+02 0.2500E-02 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.98293333E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.87302003E+03 -0.89256443E+04 0.31035357E+05 -0.49046437E+05 0.37062167E+05 Rj0 = 0.0000 54.3600 92.3100 102.5600 RKj = 0.20535697E+01 -0.18982765E+01 0.13504707E+01 0.21045359E+02



A.7 – 44


: :


1) 2)

1.5748" 3.9370"

p = lp =

2.7559" 5.9055"

cc = tp =

1.5748" 0.4724"

------------------------------


Failed at 7.194 kip shear Failed by excessive deformation of end plate and lateral bending

ct = g =


Remark

lt = 1.0472" lc = 1.0472" tbw= 0.2284" n = 2 X 2


Major parameters



Tested by Test Id.

VII - 23

0

25

50

75

100

125

150

175

200

225

250

tp

column

Moment ( kip-inch )


0

15

45

60

75

90

lc

p cc

ct p

lt

lp

n


30

tbw

g


beam

A.7 – 45



Q3 =



0.33903781E+04

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.1829E+02 0.1872E+02 0.9680E+01 0.2888E+02 3 1.03 18.75 19.09 18.87 28.50 0.1828E+02 0.1838E+02 0.1906E+02 0.2608E+02 5 2.05 37.51 37.30 38.15 52.90 0.1829E+02 0.1686E+02 0.1827E+02 0.2140E+02 7 3.08 56.26 53.19 56.02 72.44 0.1828E+02 0.1397E+02 0.1650E+02 0.1680E+02 9 4.10 75.02 65.93 71.95 87.64 0.1524E+02 0.1095E+02 0.1459E+02 0.1299E+02 11 6.15 93.77 83.86 98.48 108.46 0.1523E+02 0.6979E+01 0.1149E+02 0.7801E+01 13 7.18 112.52 90.39 109.69 115.57 0.1458E+02 0.5819E+01 0.1041E+02 0.6133E+01 15 10.26 123.28 104.86 122.32 129.34 0.3130E+01 0.3849E+01 0.3292E+01 0.3210E+01 17 17.09 139.11 124.55 139.70 142.21 0.2316E+01 0.2219E+01 0.2149E+01 0.1066E+01 19 23.93 154.28 137.29 153.98 147.14 0.2121E+01 0.1584E+01 0.2109E+01 0.4781E+00 21 30.77 168.79 146.86 169.09 149.54 0.1244E+01 0.1245E+01 0.2321E+01 0.2563E+00 23 37.61 171.29 154.59 171.17 150.90 0.3655E+00 0.1032E+01 0.3807E+00 0.1542E+00 25 44.45 174.04 161.12 174.02 151.76 0.4390E+00 0.8860E+00 0.4333E+00 0.1005E+00 27 51.28 177.04 166.79 176.89 152.33 0.3658E+00 0.7789E+00 0.3965E+00 0.6950E-01 29 58.12 179.04 171.83 179.35 152.73 0.2924E+00 0.6966E+00 0.3210E+00 0.5022E-01 31 65.64 181.54 176.79 181.44 153.06 0.3656E+00 0.6257E+00 0.4122E+00 0.3657E-01 33 73.85 184.54 181.66 184.50 153.31 0.3656E+00 0.5644E+00 0.3373E+00 0.2688E-01 35 82.05 187.54 186.09 187.04 153.51 0.2809E+00 0.5150E+00 0.2864E+00 0.2040E-01 37 90.53 189.18 190.27 189.32 153.66 0.1934E+00 0.4731E+00 0.2543E+00 0.1576E-01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.91795000E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.75677134E+02 0.71852573E+03 -0.32783283E+04 0.79395648E+04 -0.86149578E+04 Rj0 = 0.0000 7.1800 30.7700 65.6400 RKj = 0.73678812E+01 -0.52176950E+01 -0.21121374E+01 0.17739046E+00



A.7 – 46


: :


1) 2)

1.5748" 3.9370"

p = lp =

2.7559" 5.9055"

cc = tp =

1.5748" 0.4724"

------------------------------


(a) Failed at 13.5 kip shear (b) Welded after coping the beam web Failed by excessive deformation of the end plate and lateral bending

ct = g =


Remark

lt = 1.0472" lc = 1.0472" tbw= 0.2284" n = 2 X 2


Major parameters



Tested by Test Id.

VII - 24

0

45

90

135

180

225

270

315

360

405

450

tp

column

Moment ( kip-inch )


0

23

69

92

lc

p cc

ct p

lt

lp

n

115 138 161 184 207 230 Rotation ( x 1/1000 radians )

46

tbw

g


beam

A.7 – 47



Q3 =



0.37671920E+03

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3657E+02 0.1872E+02 0.3855E+02 0.2888E+02 3 0.68 25.01 12.77 23.29 19.69 0.3657E+02 0.1858E+02 0.2997E+02 0.2858E+02 5 1.54 46.88 28.39 45.38 43.51 0.1829E+02 0.1782E+02 0.2219E+02 0.2691E+02 7 3.08 68.76 53.20 72.25 80.49 0.1219E+02 0.1397E+02 0.1368E+02 0.2065E+02 9 5.13 93.77 75.92 94.16 113.12 0.1036E+02 0.8621E+01 0.8469E+01 0.1159E+02 11 8.55 118.78 97.58 117.40 137.29 0.7313E+01 0.4740E+01 0.5785E+01 0.3955E+01 13 12.82 140.65 113.58 140.00 147.16 0.3653E+01 0.3005E+01 0.4905E+01 0.1265E+01 15 17.95 161.28 126.40 163.00 151.08 0.4394E+01 0.2111E+01 0.4040E+01 0.4422E+00 17 25.64 187.54 139.91 188.70 153.02 0.2823E+01 0.1481E+01 0.2672E+01 0.1379E+00 19 38.63 222.55 155.64 222.42 153.96 0.2694E+01 0.1007E+01 0.2706E+01 0.3508E-01 21 51.28 251.30 166.80 251.93 154.24 0.2029E+01 0.7789E+00 0.2053E+01 0.1352E-01 23 61.54 270.06 174.15 271.63 154.34 0.1645E+01 0.6623E+00 0.1816E+01 0.7302E-02 25 71.80 288.81 180.50 289.58 154.40 0.1829E+01 0.5784E+00 0.1696E+01 0.4335E-02 27 82.05 307.57 186.09 306.62 154.43 0.1281E+01 0.5150E+00 0.8025E+00 0.2759E-02 29 92.31 315.07 191.10 314.66 154.46 0.7312E+00 0.4652E+00 0.7689E+00 0.1852E-02 31 102.56 322.57 195.66 322.45 154.47 0.7314E+00 0.4250E+00 0.7504E+00 0.1296E-02 33 112.82 330.07 199.89 330.08 154.48 0.7312E+00 0.3915E+00 0.7401E+00 0.9387E-03 35 123.08 337.57 203.75 337.64 154.49 0.7310E+00 0.3637E+00 0.7342E+00 0.6990E-03 37 133.34 345.07 207.36 345.16 154.50 0.9148E+00 0.3399E+00 0.7310E+00 0.5329E-03 39 143.59 356.33 210.73 356.31 154.50 0.7435E+00 0.3193E+00 0.4621E+00 0.4146E-03 41 151.80 360.10 213.27 360.10 154.51 0.4593E+00 0.3048E+00 0.4612E+00 0.3434E-03 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.13504750E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = 0.13428713E+03 -0.11162606E+03 -0.30844489E+03 0.75657836E+03 -0.61734321E+03 Rj0 = 32.1400 82.0500 133.3400 143.5900 RKj = 0.15584608E+01 -0.83166561E+00 0.35830796E+00 -0.62533627E+00



A.7 – 48


: :


1) 2)

1.5748" 3.9370"

p = lp =

2.7559" 5.9055"

cc = tp =

1.5748" 0.6299"

------------------------------


Large deformation of the column flange and stiffener were observed (a) Welded after coping the beam web (b) The comp. fla. buckled

ct = g =


Remark

lt = 1.0472" lc = 1.0472" tbw= 0.2284" n = 2 X 2


Major parameters



Tested by Test Id.

VII - 25

0

45

90

135

180

225

270

315

360

405

450

tp

column

Moment ( kip-inch )


0

7

21

28

35

42


14

tbw

g

lc

p cc

ct p

lt

lp

56

63


beam

70

n

A.7 – 49



Q3 =



0.31573608E+05

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.3540E+02 0.2966E+02 0.3497E+02 0.1132E+03 2 0.35 12.26 10.27 12.65 32.99 0.3540E+02 0.2961E+02 0.3684E+02 0.8065E+02 3 0.69 24.52 20.50 24.94 57.29 0.3540E+02 0.2944E+02 0.3364E+02 0.6107E+02 4 1.04 36.78 30.64 35.74 76.04 0.2973E+02 0.2911E+02 0.2860E+02 0.4802E+02 5 1.56 47.81 45.55 48.61 97.39 0.2123E+02 0.2819E+02 0.2117E+02 0.3520E+02 6 2.08 58.84 59.82 58.11 113.39 0.1846E+02 0.2662E+02 0.1579E+02 0.2696E+02 7 3.33 73.56 89.68 74.11 139.31 0.1068E+02 0.2091E+02 0.1153E+02 0.1604E+02 8 4.26 82.75 107.18 82.68 152.13 0.9832E+01 0.1671E+02 0.9741E+01 0.1171E+02 9 5.20 91.94 121.20 92.46 161.69 0.1105E+02 0.1346E+02 0.1110E+02 0.8940E+01 10 6.23 104.82 133.78 104.44 169.84 0.1240E+02 0.1089E+02 0.1177E+02 0.6881E+01 11 7.27 117.70 144.09 116.55 176.21 0.1121E+02 0.9080E+01 0.1140E+02 0.5463E+01 12 8.83 132.41 156.72 133.14 183.53 0.9435E+01 0.7234E+01 0.9782E+01 0.4040E+01 13 10.39 147.11 166.97 147.04 189.06 0.8320E+01 0.6011E+01 0.8133E+01 0.3111E+01 14 12.12 159.37 176.51 160.08 193.80 0.7080E+01 0.5066E+01 0.7082E+01 0.2412E+01 15 13.85 171.63 184.66 172.06 197.53 0.7080E+01 0.4385E+01 0.6554E+01 0.1926E+01 16 15.59 183.89 191.79 183.57 200.55 0.7080E+01 0.3871E+01 0.6784E+01 0.1574E+01 17 17.32 196.15 198.13 195.58 203.04 0.7080E+01 0.3471E+01 0.7071E+01 0.1311E+01 18 19.05 208.41 203.85 207.94 205.13 0.7080E+01 0.3150E+01 0.7158E+01 0.1109E+01 19 20.78 220.67 209.07 220.19 206.90 0.7075E+01 0.2886E+01 0.6941E+01 0.9507E+00 20 22.86 235.38 214.80 234.02 208.72 0.6190E+01 0.2626E+01 0.6290E+01 0.8017E+00 21 24.94 246.41 220.02 247.71 210.26 0.5312E+01 0.2412E+01 0.6090E+01 0.6856E+00 22 27.01 257.44 224.84 259.20 211.58 0.4868E+01 0.2233E+01 0.4963E+01 0.5930E+00 23 29.09 266.63 229.32 268.31 212.74 0.4425E+01 0.2081E+01 0.3802E+01 0.5181E+00 24 31.17 275.83 233.50 275.05 213.75 0.6276E+01 0.1949E+01 0.2700E+01 0.4566E+00 25 32.41 285.02 235.93 284.96 214.29 0.7386E+01 0.1877E+01 0.7663E+01 0.4249E+00 26 33.66 294.22 238.18 294.15 214.81 0.7104E+01 0.1813E+01 0.7103E+01 0.3964E+00 27 35.01 303.42 240.63 303.37 215.32 0.6799E+01 0.1747E+01 0.6553E+01 0.3686E+00 28 36.37 312.61 242.91 311.90 215.80 0.6381E+01 0.1688E+01 0.6065E+01 0.3437E+00 29 37.92 321.81 245.54 320.96 216.32 0.5900E+01 0.1622E+01 0.5575E+01 0.3179E+00 30 39.48 331.00 247.97 329.32 216.80 0.5141E+01 0.1564E+01 0.5160E+01 0.2950E+00 31 41.56 339.58 251.15 339.55 217.38 0.4129E+01 0.1493E+01 0.4708E+01 0.2681E+00 32 43.64 348.16 254.18 348.95 217.91 0.4129E+01 0.1428E+01 0.4357E+01 0.2448E+00 33 45.72 356.74 257.15 357.72 218.40 0.4129E+01 0.1367E+01 0.4087E+01 0.2243E+00 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.46754167E+00 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 4 AI = -0.27180865E+03 0.51427072E+04 -0.28874308E+05 0.70637209E+05 -0.77818232E+05 Rj0 = 3.3300 13.8500 22.8600 31.1700 RKj = -0.27143953E+01 -0.30702735E+00 0.76162437E+00 0.55709010E+01



A.7 – 50


: :


1) 2)

1.5748" 3.9370"

p = lp =

2.7559" 5.9055"

cc = tp =

1.5748" 0.6299"

------------------------------


Large deformation at the column flange Welded after coping the beam web

ct = g =


Remark

lt = 1.0472" lc = 1.0472" tbw= 0.2284" n = 2 X 2


Major parameters



Tested by Test Id.

VII - 26

0

40

80

120

160

200

240

280

320

360

400

tp

column

Moment ( kip-inch )


0

18

54

72

90

lc

p cc

ct p

lt

lp

n


36

tbw

g


beam

A.7 – 51



Q3 =



0.70582005E+04

-10

---------------------------------------------------------------------------------------------------------------------------No Rotation Moment Connection stiffness (radians) (kip-inch) (kip-inch) X 1000 X 1/1000 Expri. Poly. M.Expo. P.Model. Expri. Poly. M.Expo. P.Model. ---------------------------------------------------------------------------------------------------------------------------1 0.00 0.00 0.00 0.00 0.00 0.2213E+02 0.2966E+02 0.2488E+02 0.5407E+02 3 1.11 24.52 32.65 24.98 49.05 0.2213E+02 0.2902E+02 0.2067E+02 0.3576E+02 5 2.08 45.98 59.82 43.94 78.53 0.2210E+02 0.2662E+02 0.1859E+02 0.2578E+02 7 3.33 64.36 89.63 65.94 105.33 0.1106E+02 0.2092E+02 0.1677E+02 0.1790E+02 9 4.66 82.75 113.47 87.10 125.50 0.1838E+02 0.1522E+02 0.1503E+02 0.1281E+02 11 5.70 104.81 127.57 101.99 137.37 0.2389E+02 0.1211E+02 0.1361E+02 0.1018E+02 13 8.31 132.40 152.80 132.49 158.25 0.7079E+01 0.7765E+01 0.9634E+01 0.6243E+01 15 14.54 156.31 187.61 156.30 183.75 0.2213E+01 0.4163E+01 0.3996E+01 0.2673E+01 17 22.34 171.01 213.42 171.78 198.23 0.1515E+01 0.2686E+01 0.1182E+01 0.1287E+01 19 31.17 183.89 233.51 182.43 206.64 0.1594E+01 0.1949E+01 0.1679E+01 0.7043E+00 21 41.56 202.28 251.15 204.45 212.23 0.2947E+01 0.1493E+01 0.2490E+01 0.4105E+00 23 46.76 220.67 258.50 218.99 214.13 0.3302E+01 0.1341E+01 0.3061E+01 0.3277E+00 25 57.15 246.41 271.21 246.37 216.94 0.2123E+01 0.1121E+01 0.2098E+01 0.2223E+00 27 65.45 262.96 279.97 262.98 218.56 0.1772E+01 0.9940E+00 0.1771E+01 0.1705E+00 29 70.65 281.35 284.96 281.35 219.38 0.6187E+01 0.9296E+00 0.6182E+01 0.1467E+00 31 76.89 299.74 290.55 299.77 220.22 0.1327E+01 0.8635E+00 0.8905E+00 0.1241E+00 33 85.20 307.70 297.41 306.77 221.15 0.5894E+00 0.7900E+00 0.7970E+00 0.1013E+00 35 93.51 312.60 303.72 313.07 221.92 0.6428E+00 0.7291E+00 0.7204E+00 0.8414E-01 37 103.90 319.97 310.96 320.19 222.71 0.7080E+00 0.6661E+00 0.7018E+00 0.6816E-01 39 114.29 327.32 317.66 327.26 223.35 0.7080E+00 0.6136E+00 0.6632E+00 0.5630E-01 ----------------------------------------------------------------------------------------------------------------------------


Modified exponential model : Bm = Sum ( Ai X ( 1 - exp( - R/( 2*i*C ) ) ) ) + Sum ( RKj X ( R - Rj0 ) ) + Bm0 C = 0.10909167E+01 Bmo= 0.00000000E+00 Nexp= 6 Nliner= 10 AI = 0.74905472E+02 -0.25071099E+03 -0.35123669E+04 0.14964317E+05 -0.18209656E+05 Rj0 = 10.3900 14.5400 18.7000 36.3700 51.9500 62.3400 68.5700 70.6500 72.7300 103.9000 RKj = -0.19237258E+01 0.47297899E+01 0.13115126E+01 -0.89989999E+00 -0.14819585E+01 -0.38362559E+00 0.44455713E+01 0.85670509E+00 -0.60817041E+01 0.46927896E-01



A.7 – 52


Index A AISC. See American Institute of Steel Construction AISC classification system (AISC 2005), 6–8, 7 AISC specification, 5, 22–26 connection classification, 22–23 introduction to, 22 structural analysis and design for frames with PR connections, 23–26 Allowable stress design (ASD), 95 American Institute of Steel Construction (AISC), 28, 148 ASD. See Allowable stress design (ASD) B Beam, semi-rigid connections at both ends, 7 Beam-column approach, 165–167 Beams, effects of semi-rigid connections on, 40–45 beams with semi-rigid connections, 43–45 lateral torsional buckling load for compact beams, 41–43 Beam-to-column connections, 22, 79–80 Bending moments, 144–145 Bjorhovde et al. classification system, 8–9 Bolted connections, 144 Bolt Forces Pri, potential, 224–226 Bolt shear/bolt tension, 30 Bounding line model, 87 Bounding surface model with internal variable, 90–92 Bowing matrix, kb, 254 Bowstring column, 195–199 cable pretension force, 197–198 length of horizontal strut, 198–199 pretensioned steel column, 195 spacing of horizontal strut, 199 structural configurations, 195–197

Bowstring frame, 199–206 effects of pretension, 205–206 nonlinear analysis, 204–205 structural layout, 199–201 testing of mullion-to-transom and transomto-hanger connections, 201–204 Braced vs. unbraced frames, 145–147 Buckling load comparison, semi-rigid portal frame, 53 Building core wall, modeling of, 219–221 C Cable pretension force, 197–198 Case studies for second-order (direct) analysis of semi-rigid frames in Hong Kong, 255–269 conclusions, 268 examples, 259–268 introduction, 255–256 modeling of semi-rigid jointed members, 257–259 second-order integrated design and analysis, 256–257 CFTs. See Concrete-filled tubes (CFTs) Classification of connections, 1–22 AISC classification system (AISC 2005), 6–8 Bjorhovde et al. classification system, 8–9 classification systems, comparison of existing, 21–22 Eurocode 3 classification system, 1–6 general remarks, 1–2 Goto et al. classification system, 11–20 Nethercot et al. classification system, 9–11 rotational deformation of a connection, 1, 2 Classification systems, comparison of existing, 21–22 I–1

I–2

Code of Practice for Structural Uses of Steel Hong Kong, The (COPHK), 255, 261, 263–264 Code of Practice on Wind Effects in Hong Kong, 264 Column(s) flange failure modes, 224 leaning/non-leaning, 38 strength design equations, 39–40 Columns, effects of semi-rigid connections on, 32–41 column effective length factor, 32–35 column strength design equations, 39–40 K factor for columns in semi-rigid frames, 35–37 K factor computation, other approaches for, 38–39 procedure for evaluating K using the modified moment of inertia approach, 38 Component fractures, 30 Composite beam, modeling of, 217–219 Composite column, modeling of, 216–217 Composite frames, advanced analysis of, 211–241 20-story steel frame with composite beams, analysis of, 234–237 building core wall, modeling of, 219–221 composite beam, modeling of, 217–219 composite column, modeling of, 216–217 composite members, 212–216 composite semi-rigid end-plate connection, modeling of, 221–234 core-braced multistory frame, 238–241 Composite haunch connection under negative moment, 223 Composite members, advanced analysis of, 212–216 distortional buckling, 214–215 lateral torsional buckling, 215 limited slip capacity, 215, 216 local and overall buckling, 212–214 rotational capacities, 216 Composite semi-rigid end-plate connection, 221–234 Computer method of analysis, 260–261, 266 Concrete-filled tubes (CFTs), 217 Connection, defined, 27. See also Classification of connections


Connection behavior, 28–32 connection rotational ductility, 30–32 connection stiffness, 30 connection strength, 30 loading/unloading behavior, semi-rigid connections, 29 moment rotation behavior, semi-rigid connections, 29 Connection ductility, 23–24 Connection hinges, formation of, 54–55 Connection moment rotation behavior, 55 Connection-moment strength Mn, 24 Connections in building frame, 185–190 component method, 188–189 computer implementation, 190 Connection stiffness, 21, 23 Connection strength, 21–22, 23 Connection types, 97. See also Parameter definition for connection type Constant load Newton-Raphson method, 261 COPHK. See Code of Practice for Structural Uses of Steel Hong Kong, The (COPHK) Core, 143, 236, 237 Core-braced multistory frame, analysis of, 238–242 core-braced frames with strong core walls, 238–240 core-braced frames with weak core walls, 240–241 second-order effects in the core-braced frame, 241 Core wall, 219–220 Curve-fitting techniques, 30 Cyclic loading, behavior under, 89–92 bounding surface model, 92 independent hardening model, 89 kinematic hardening model, 90–91 D Design of semi-rigid frames, 56–64. See also Semi-rigid frame(s) sway-permitted semi-rigid frames, 60–64 sway-prevented semi-rigid frames, 56–60 Direct analysis approach, 153–154 Discretization, 217 Distortional buckling, 214–215 Dome. See Hemispherical dome on the roof of a building

Index

Double web-angle (DWA) connections, 71–73, 103–105, 240–241 Drift of semi-rigid frames, 64–67 load cases, 66 portal frame, design of, 65 prediction formulas, 65 Ductility demand, 32 DWA. See Double web-angle (DWA) connections E EC3 classification of connections by stiffness, 4 classification of connections by strength, 6 connection models, 4 load-carrying capacity of frames, 5 EEP. See Extended end-plate (EEP) connections Effects of semi-rigid connections on structural members and frames, 27–70 beams, effects on, 40–45 columns, effects on, 32–41 connection behavior, 28–32 frames, effects on, 45–67 introduction to, 27–28 summary/conclusions, 67–68 Elastic bifurcation analysis of semi-rigid frames, 46–52 2-D column element, 49 beam stiffness relationship, 46–49 buckling analysis, semi-rigid portal frame, 52 column stiffness relationship, 49–52 Elastic-plastic structural analysis, 3–4 Elastic stiffness matrix, ke, 252 End-plate bending, failure modes, 224 End-restrained elastic column, 33 ETABS, 241 Eurocode 3 classification system, 1–6, 148, 153–154, 221, 255. See also EC3 Exponential model, 82–86 Extended end-plate (EEP) connections, 75, 76, 114–123, 240–241 F Fastening mode patterns, 99 Finite element method, 219 Fire analysis of semi-rigid frame, 206–211 Flush end-plate connections, 75, 76, 123–127 FORTRAN77, 130 FORTRAN compiler, 129

I–3

Four-story frame, comparative analysis, 55 FR. See Fully restrained (FR) connection Frame imperfections, 257 Frames, effects of semi-rigid connections on, 45–67 analysis of semi-rigid frames, 45–55 design of semi-rigid frames, 56–64 drift of semi-rigid frames, 64–67 Frame stability, 151–154 behavioral effects, 152 direct analysis approach, 153–154 imperfection effects, 151–152 limit states design, 153 second-order analysis, 153 Frames with PR connections, structural analysis/design, 24–26 Frye-Morris model, 81–82, 97, 129 Fully restrained (FR) connection, 6, 22, 24, 25 G Geometric stiffness matrix, kg, 253 Goto et al. classification system, 11–20 curve-fitting coefficients, 18, 19, 20 equilibrium curves of subassemblages with connections classified as rigid, 16 imperfections and material properties of subassemblages, 17 for initial stiffness of connections, 14 multistory multibay frames, 11, 12 subassemblages, 13 three-parameter power model, 15 H Hardening model independent, 89 kinematic, 90–91 Header end-plate connections, 75 Header plate connections, 75, 77, 127–129 Hemispherical dome on the roof of a building, 259–264 boundary conditions, 262 computer method of analysis, 260–261 connection stiffness, 262–263 design code, 261–262 imperfections, 263–264 load carrying capacity, 264 load path, 260 structure description, 259–260 vibration frequency, additional, 264

I–4

High-rise buildings, 211, 216. See also Multistory frame Hogging (negative) moment region, 211 Horizontal strut length of, 198–199 spacing of, 199 I Imperfections, 152–153, 257, 263–264 Incipient instability, 36 Initial imperfections, 257 Initial rotational stiffness, 232 Initial stiffness Rki, 30 J Joint classification, 149 Joint representation, 148–149 K K-factor calculation, 39 K factor computation, other approaches for, 38–39 K factor for columns in semi-rigid frames, 35–40 sway-permitted frames, 36–37 sway-prevented frames, 35, 36 Kishi-Chen database, 97 L Lateral torsional buckling of composite members, 215 modeling of, 179 Leaning columns, 38 Limited slip capacity, 215–216 Limit-state design method, 95, 153 Linear model, 80–81 Linear theory, fundamental, 219 Load and resistance factor design (LRFD), 95–96 Load and Resistance Factored Design Specification for Structural Steel Buildings, 148 Load-carrying capacity, 5, 268 Load deflection analysis of semi-rigid frames, 52–54 Load path, 260, 265–266 Local and overall buckling of composite members, 213–214 Local buckling, modeling of, 179–180


LRFD. See Load and resistance factor design (LRFD) M Marchant-Rankin formula, 4, 5 Material properties of steel, 261–262 Member bowing effect, 165–167 Member imperfections, 257 Modeling of building core wall, 219–221 of composite beam, 217–219 of composite column, 216–217 of composite semi-rigid end-plate connection, 221–234 of lateral-torsion buckling, 179 of local buckling, 179–180 of semi-rigid connections, 185–190 of semi-rigid jointed members, 257–259 of truss element, 184–185 Modeling of connections, 79–94 cyclic loading, behavior under, 89–82 general remarks, 79–80 monotonic loading, behavior using, 80–89 Modeling of material nonlinearity in beamcolumn, 170–180 concentrated plastic-hinge formulation, 173–174 methods for modeling material non linearity, 170–172 numerical strategies for plastic-hinge analysis, 175–178 plastic strength surface, 172–173 two-surface plastic-hinge formulation, 174–175 Modeling of tubular joints, 190–193 joint capacity, 190–191 load-deformation relationship, 192–193 parametric equations for local joint flexibility, 191–192 Modified exponential model, 97, 129 Modified moment of inertia approach, procedure for evaluating K, 38 Moment capacity, 232 Moment resistance, 221–229 equivalent T-stubs, 224 failure modes for column flange or endplate bending, 224 negative moment capacity, 222–223 panel zone shear resistance, 228–229

Index

positive moment capacity, 226–228 potential bolt forces Pri, determination of, 224–226 Moment-rotation (M–θr) curves, 1, 2, 3 Moment-rotation response, classification of, 25 Monotonic loading, 32 Monotonic loading, behavior under, 80–89 bounding line model, 87, 88 exponential model, 82–86 linear model, 80–81 polynomial model, 81–82 power model, 86–87 Ramberg-Osgood model, 87, 88 Richard-Abbot model, 88–89 M–θr curves for each connection type, experimental, 98–99 Mullion-to-transom connections, testing of, 201–204 Multistory, multibay frames, deformation pattern, 12 Multistory frame, 234–241 20-story steel frame with composite beams, analysis of, 234–237 core-braced multistory frame, 238–241 pinned connections, steel frames and, 144 Multistory multibay frames, 11, 12 N Negative moment capacity, 222–223 Nethercot et al. classification system, 9–11 Newton-Raphson method, 261 Nominal moment capacity (Mcn), 30 Non-leaning columns, 38 Nonsway frames. See Sway-prevented frames Nonsway frames, subassemblage of, 10 P Panel zone shear resistance, 228–229 Parameter definition for connection type, 100–129 double web-angle connections, 103–105 extended end-plate connections, 110–123 flush end-plate connections, 123–127 header plate connections, 127–129 single web-angle connections/single plate connections, 100–102 top- and seat-angle connections, 110 top- and seat-angle with double web-angle connections, 106–109

I–5

Parametric techniques, 30 Partially restrained (PR) connections, 6, 22, 25. See also PR connection types Partial-strength semi-rigid connections, 32 P-Δ and Pδ effects, 256–257 Piecewise multilinear model, 80, 81 Pin-based portal frame, 5 Pin-ended column. See Columns, effects of semi-rigid connections on Pin-jointed frames, 144 Plastic-hinge analysis, numerical strategies for, 175–178 control of deviation of yield surface, 178 elastic unloading at plastic hinge, 175 formation of plastic hinge within the member length, 176–177 load increment control, 177 plastic hinges at common node adjoining two elements, 175–176 pure axial plasticity, 175 Plastic-hinge formulation, 173–175 concentrated, 173–174 two-surface, 174–175 Plastic hinges, formation of, 54–55, 234 Plasticity formulation at elevated temperature, 178–179 Plastic Neutral Axis (PNA), 222, 223 Plastic strength surface, 172–173 PNA. See Plastic Neutral Axis (PNA) Polynomial model, 81–82 Portal frame load types and, 53 pin-based, 5 Positive moment capacity, 226–228 Potential Bolt Forces Pri, 224–226 Power model, 15, 86–87, 87 PR. See Partially restrained (PR) connections PR connection types, 71–77. See also Partially restrained (PR) connections double web-angle connections, 71–73 extended end-plate connections/flush endplate connections, 75, 76 header-plate connections, 75, 77 single web-angle connections/single plate connections, 71 top- and seat-angle connections, 73–74 top- and seat-angle connections with double web-angle, 73 Preloads, 216–217

I–6

Pretension, effects of, 205–206 Pretensioned steel column, 195 R Ramberg-Osgood model, 87, 88 RC. See Reinforced concrete (RC) Reinforced concrete (RC), 260 Richard-Abbot model, 86, 88–89 Rigid frames, 144 Roof. See Hemispherical dome on the roof of a building; Shallow roof at the top of a building Rotational capacity, composite members and, 215–216 Rotational deformation of a connection, 96 Rotational stiffness, 229–232 under negative movement, 229–231 under positive movement, 231 Rotation capacity of connections, AISC and, 8 connection strength and, 21–22 S Sagging (positive) moment region, 211 Second-order analysis, 153 Second-order effects in the core-braced frame, 241 Second-order integrated design and analysis, 256–257 frame imperfections, 257 imperfections, initial, 257 member imperfections, 257 P-Δ and P-δ effects, 256, 257 Seismic loads, 32 Semi-rigid connection database, 132 Semi-rigid connections. See Effects of semirigid connections on structural members and frames Semi-rigid connections on beams. See Beams, effects of semi-rigid connections on Semi-rigid frame(s). See also Design of semirigid frames analysis/design of, 45–55, 150–151 with connections undergoing loading and unloading, 31 drift of, 64–67 elastic bifurcation analysis of, 46–52 fire analysis of, 206–211


sway-permitted, 60–64 sway-prevented, 56–60 Semi-rigid jointed members, modeling of, 257–259 Serviceability limit state, classification at, 9, 10 Serviceability checks, 240 Service load moment, 30 Shallow roof at the top of a building, 264–268 boundary conditions, 267 computer method of analysis, 266 connection stiffness, 267 design code, 266–267 imperfections, 267–268 load carrying capacity, 268 load path, 265–266 structure description, 264–265 vibration frequency, additional, 268 Shear walls, 143 Simple beam, semi-rigid connections at both ends, 7 Simple connections, 6 Simple frames, 144–145 Single-span subframe under uniformly distributed beam load, 11 Single web-angle connections/single plate connections, 71, 72, 76, 100–102 Slip capacity, limited, 215–216 Spring model, 229–230 Stability interpolation functions, 162–163 Steel, material properties of, 261–262 Steel and composite semi-rigid frames, advanced analysis of, 143–254 bowing matrix, kb, 254 composite frames, 211–241 elastic stiffness matrix, ke, 252 geometric stiffness matrix, kg, 253 steel frames, 154–211 structural frames, 143–154 Steel-concrete composite connections Steel Connection Data Bank (SCDB) program, 97, 129–132 bank.d output file, 130, 133–139 examples, 131–132 fastening mode patterns, 131 files used in program, 131 input data, 130 outline of, 129–130 user manual for, 130–131

Index

Steel connection database, 95–142 general remarks, 95–99 parameter definition for connection type, 100–129 steel connection databank program, 129–132 Web site of connections, 132–139 Steel frames, advanced analysis of, 154–211 bowstring column, 195–199 bowstring frame, 199–206 development of, 154–157 element forces/geometry in beam-column, 180–184 fire analysis, semi-rigid frame, 206–211 lateral torsional buckling, modeling, 180 local buckling, modeling of, 179–180 material nonlinearity in beam-column, modeling of, 170–179 semi-rigid connections, modeling, 185–190 stiffness formulation of beam-column, 157–169 truss element, modeling of, 184–185 tubular frame with K-type joints, 193–195 tubular joints, modeling of, 190–193 Stiffness coefficient, 230–231 Stiffness formulation of beam-column, 157–169 available stiffness formulations, 157–158 beam-column approach/member bowing effect, 165–167 elastic and geometric stiffness matrices, 163–165 stability and bowing functions, 167–168 stability interpolation functions, 162–163 tangent stiffness matrix, 168–169 virtual work equation, 158–162 Structural frames, 143–154 braced vs. unbraced frames, 145–147 joint representation, 148–149 rigid frames, 144 semi-rigid frames, analysis/design of, 150–151 simple frames, 144–145 stability of frame, 151–154 sway vs. nonsway frames, 147–148 Structural steel, types of, 261–262 Subassemblage of nonsway frames, 10 Sway-permitted frames, 36–37, 147–148

I–7

Sway-permitted semi-rigid frames, 60–64 beams, design of, 62–63 bending moment diagrams, 62 column end moments, determination of, 64 columns, design of, 64 Rki and Mu, determination of, 63 semi-rigid frame assemblage, 61 states of moments in connections, 61 Sway-prevented frames, 35, 36, 147–148 Sway-prevented semi-rigid frames, 56–60 deflection/connection stiffness, relationship between, 59 design of beams, 56–59 design of columns, 60 end restraint on beam moments and deflection, 56 load effects on partially restrained beam, 57 moments/connection stiffness, relationships between, 58 T Tangent stiffness matrix, 168–169 Thin-walled members, 219, 220 Three-parameter power model, 15, 97, 129 Top- and seat-angle connections, 73, 74, 76, 110, 111–114 Top- and seat-angle with double web-angle (TSAW) connections, 73, 74, 106–109, 240–241 Torsional deformation, 220–221 Transom-to-hanger connections, testing of, 201–204 Triangulated vertical truss, 145, 146 Truss element, modeling of, 184–185 TSAW. See Top- and seat-angle with double web-angle (TSAW) connection T-stubs, equivalent, 224 Tubular frame with K-type joints, 193–195 20-story steel frame with composite beams, analysis of, 234–237 load-deflection curves, 235 multistory frame, strong core, 236 multistory frame, weak core, 237 Type-2 connections, 144 U Ultimate-limit state, 5, 9, 10 Ultimate stiffness Rku, 30

I–8

Updating of element forces and geometry in beam-column, 180–184 force recovery based on the natural deformation approach, 180–182 geometry updating and web-plane vector, 182–184 V Vertical truss, triangulated, 145, 146 Vibration frequency, 264, 268 Virtual work equation, 158–162


W Warping deformation, 220–221 Web site, steel connection database, 132–139 Welded connections, 144 Weld fractures, 30 Wind-moment design, 144

Semi-rigid Connections Handbook - Wai-Fah Chen

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